Adams, Scot
2001-01-01
Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of the
Robinson manifolds and Cauchy-Riemann spaces
Trautman, A
2002-01-01
A Robinson manifold is defined as a Lorentz manifold (M, g) of dimension 2n >= 4 with a bundle N subset of C centre dot TM such that the fibres of N are maximal totally null and there holds the integrability condition [Sec N, Sec N] subset of Sec N. The real part of N intersection N-bar is a bundle of null directions tangent to a congruence of null geodesics. This generalizes the notion of a shear-free congruence of null geodesics (SNG) in dimension 4. Under a natural regularity assumption, the set M of all these geodesics has the structure of a Cauchy-Riemann manifold of dimension 2n - 1. Conversely, every such CR manifold lifts to many Robinson manifolds. Three definitions of a CR manifold are described here in considerable detail; they are equivalent under the assumption of real analyticity, but not in the smooth category. The distinctions between these definitions have a bearing on the validity of the Robinson theorem on the existence of null Maxwell fields associated with SNGs. This paper is largely a re...
Seeley-De Witt coefficients in a Riemann-Cartan manifold
International Nuclear Information System (INIS)
Cognola, G.; Zerbini, S.; Istituto Nazionale di Fisica Nucleare, Povo
1988-01-01
A new derivation of the first two coefficients of the heat kernel expansion for a second-order elliptic differential operator on a Riemann-Cartan manifold with arbitrary torsion is given. The expressions are presented in a very compact and tractable form useful for physical applications. Comparisons with other similar results that appeared in the literature are briefly discussed. (orig.)
Bui-Thanh, T.; Girolami, M.
2014-11-01
We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint
International Nuclear Information System (INIS)
Rogers, Alice
1990-01-01
A super Riemann surface is a particular kind of (1,1)-dimensional complex analytic supermanifold. From the point of view of super-manifold theory, super Riemann surfaces are interesting because they furnish the simplest examples of what have become known as non-split supermanifolds, that is, supermanifolds where the odd and even parts are genuinely intertwined, as opposed to split supermanifolds which are essentially the exterior bundles of a vector bundle over a conventional manifold. However undoubtedly the main motivation for the study of super Riemann surfaces has been their relevance to the Polyakov quantisation of the spinning string. Some of the papers on super Riemann surfaces are reviewed. Although recent work has shown all super Riemann surfaces are algebraic, some areas of difficulty remain. (author)
The continuous determination of spacetime geometry by the Riemann curvature tensor
International Nuclear Information System (INIS)
Rendall, A.D.
1988-01-01
It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)
Conformal mapping on Riemann surfaces
Cohn, Harvey
2010-01-01
The subject matter loosely called ""Riemann surface theory"" has been the starting point for the development of topology, functional analysis, modern algebra, and any one of a dozen recent branches of mathematics; it is one of the most valuable bodies of knowledge within mathematics for a student to learn.Professor Cohn's lucid and insightful book presents an ideal coverage of the subject in five pans. Part I is a review of complex analysis analytic behavior, the Riemann sphere, geometric constructions, and presents (as a review) a microcosm of the course. The Riemann manifold is introduced in
Indian Academy of Sciences (India)
the basis for various fields of mathematics and the general relativity theory of Einstein. In 1857 ... This idea explained the work on algebraic ... theory, Riemann found the key to the problem of the distribution of primes, in that he associated it ...
Differential geometry of quasi-Sasakian manifolds
International Nuclear Information System (INIS)
Kirichenko, V F; Rustanov, A R
2002-01-01
The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann-Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann-Christoffel tensor are discovered and used for distinguishing a new class of CR 1 quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the B-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Quantum Riemann surfaces. Pt. 2; The discrete series
Energy Technology Data Exchange (ETDEWEB)
Klimek, S. (Dept. of Mathematics, IUPUI, Indianapolis, IN (United States)); Lesniewski, A. (Dept. of Physics, Harvard Univ., Cambridge, MA (United States))
1992-02-01
We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of C{sup *}-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional C{sup *}-algebras. (orig.).
Anomalous Lorentz and CPT violation
Klinkhamer, F. R.
2018-01-01
If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined over a spacetime manifold with topology ℛ3 × S 1 and periodic spin structure for the compact dimension. It can be shown that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. For arbitrary Abelian U(1) gauge fields with trivial holonomies in the compact direction, this anomalous Lorentz and CPT violation has recently been established perturbatively with a Pauli-Villars-type regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
Riemann, topology, and physics
Monastyrsky, Michael I
2008-01-01
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...
International Nuclear Information System (INIS)
Pokhozhaev, Stanislav I
2011-01-01
The notion of Riemann quasi-invariants is introduced and their applications to several conservation laws are considered. The case of nonisentropic flow of an ideal polytropic gas is analysed in detail. Sufficient conditions for gradient catastrophes are obtained. Bibliography: 16 titles.
International Nuclear Information System (INIS)
Arnlind, Joakim; Hofer, Laurent; Hoppe, Jens; Bordemann, Martin; Shimada, Hidehiko
2009-01-01
We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear, Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For a continuous class of quartic constraints, we explicitly work out finite dimensional representations of the corresponding C-Algebras.
International Nuclear Information System (INIS)
Finkelstein, D.; Finkelstein, S.R.; Holm, C.
1986-01-01
Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist
Sinha, Rajnikant
2014-01-01
This book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard’s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book ...
Hempel, John
2004-01-01
A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. -Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The t
Deformations of super Riemann surfaces
International Nuclear Information System (INIS)
Ninnemann, H.
1992-01-01
Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.)
Deformations of super Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Ninnemann, H [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
1992-11-01
Two different approaches to (Konstant-Leites-) super Riemann surfaces are investigated. In the local approach, i.e. glueing open superdomains by superconformal transition functions, deformations of the superconformal structure are discussed. On the other hand, the representation of compact super Riemann surfaces of genus greater than one as a fundamental domain in the Poincare upper half-plane provides a simple description of super Laplace operators acting on automorphic p-forms. Considering purely odd deformations of super Riemann surfaces, the number of linear independent holomorphic sections of arbitrary holomorphic line bundles will be shown to be independent of the odd moduli, leading to a simple proof of the Riemann-Roch theorem for compact super Riemann surfaces. As a further consequence, the explicit connections between determinants of super Laplacians and Selberg's super zeta functions can be determined, allowing to calculate at least the 2-loop contribution to the fermionic string partition function. (orig.).
Kosinski, Antoni A
2007-01-01
The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho
Computational approach to Riemann surfaces
Klein, Christian
2011-01-01
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first...
Moduli of Riemann surfaces, transcendental aspects
International Nuclear Information System (INIS)
Hain, R.
2000-01-01
These notes are an informal introduction to moduli spaces of compact Riemann surfaces via complex analysis, topology and Hodge Theory. The prerequisites for the first lecture are just basic complex variables, basic Riemann surface theory up to at least the Riemann-Roch formula, and some algebraic topology, especially covering space theory. The first lecture covers moduli in genus 0 and genus 1 as these can be understood using relatively elementary methods, but illustrate many of the points which arise in higher genus. The notes cover more material than was covered in the lectures, and sometimes the order of topics in the notes differs from that in the lectures. We have seen in genus 1 case that M 1 is the quotient Γ 1 /X 1 of a contractible complex manifold X 1 = H by a discrete group Γ 1 = SL 2 (Z). The action of Γ 1 on X 1 is said to be virtually free - that is, Γ 1 has a finite index subgroup which acts (fixed point) freely on X 1 . In this section we will generalize this to all g >= 1 - we will sketch a proof that there is a contractible complex manifold Xg, called Teichmueller space, and a group Γ g , called the mapping class group, which acts virtually freely on X g . The moduli space of genus g compact Riemann surfaces is the quotient: M g = Γ g /X g . This will imply that M g has the structure of a complex analytic variety with finite quotient singularities. Teichmueller theory is a difficult and technical subject. Because of this, it is only possible to give an overview. In this lecture, we compute the orbifold Picard group of M g for all g >= 1. Recall that an orbifold line bundle over M g is a holomorphic line bundle L over Teichmueller space X g together with an action of the mapping class group Γ g on it such that the projection L → X g is Γ g -equivariant. An orbifold section of this line bundle is a holomorphic Γ g -equivariant section X g → L of L. This is easily seen to be equivalent to fixing a level l>= 3 and considering holomorphic
International Nuclear Information System (INIS)
Wiliardy, Abednego; Gunara, Bobby Eka
2016-01-01
An n dimensional flat manifold N is embedded into an n +1 dimensional stationary manifold M. The metric of M is derived from a general form of stationary manifold. By taking several assumption, such as 1) the ambient manifold M to be maximally symmetric space and satisfying a pure gauge condition, and 2) the submanifold is taken to be flat, then we find the solution that satisfies Ricci scalar of N . Moreover, we determine whether the solution is compatible with the Ricci and Riemann tensor of manifold N depending on the dimension. (paper)
Morrow, James
2006-01-01
This book, a revision and organization of lectures given by Kodaira at Stanford University in 1965-66, is an excellent, well-written introduction to the study of abstract complex (analytic) manifolds-a subject that began in the late 1940's and early 1950's. It is largely self-contained, except for some standard results about elliptic partial differential equations, for which complete references are given. -D. C. Spencer, MathSciNet The book under review is the faithful reprint of the original edition of one of the most influential textbooks in modern complex analysis and geometry. The classic
Poisson sigma model with branes and hyperelliptic Riemann surfaces
International Nuclear Information System (INIS)
Ferrario, Andrea
2008-01-01
We derive the explicit form of the superpropagators in the presence of general boundary conditions (coisotropic branes) for the Poisson sigma model. This generalizes the results presented by Cattaneo and Felder [''A path integral approach to the Kontsevich quantization formula,'' Commun. Math. Phys. 212, 591 (2000)] and Cattaneo and Felder ['Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model', Lett. Math. Phys. 69, 157 (2004)] for Kontsevich's angle function [Kontsevich, M., 'Deformation quantization of Poisson manifolds I', e-print arXiv:hep.th/0101170] used in the deformation quantization program of Poisson manifolds. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P n with particular ''alternating'' boundary conditions. In the presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero mode contributions
Supermanifolds and super Riemann surfaces
International Nuclear Information System (INIS)
Rabin, J.M.
1986-09-01
The theory of super Riemann surfaces is rigorously developed using Rogers' theory of supermanifolds. The global structures of super Teichmueller space and super moduli space are determined. The super modular group is shown to be precisely the ordinary modular group. Super moduli space is shown to be the gauge-fixing slice for the fermionic string path integral
Searching for Lorentz violation
International Nuclear Information System (INIS)
Allen, Roland E.; Yokoo, Seiichirou
2004-01-01
Astrophysical, terrestrial, and space-based searches for Lorentz violation are very briefly reviewed. Such searches are motivated by the fact that all superunified theories (and other theories that attempt to include quantum gravity) have some potential for observable violations of Lorentz invariance. Another motivation is the exquisite sensitivity of certain well-designed experiments and observations to particular forms of Lorentz violation. We also review some new predictions of a specific Lorentz-violating theory: If a fundamental energy m-bar c2 in this theory lies below the usual GZK cutoff E GZK , the cutoff is shifted to infinite energy; i.e., it no longer exists. On the other hand, if m-bar c2 lies above E GZK , there is a high-energy branch of the fermion dispersion relation which provides an alternative mechanism for super-GZK cosmic-ray protons
Flux quantization and quantum mechanics on Riemann surfaces in an external magnetic field
International Nuclear Information System (INIS)
Bolte, J.; Steiner, F.
1990-10-01
We investigate the possibility to apply an external constant magnetic field to a quantum mechanical system consisting of a particle moving on a compact or non-compact two-dimensional manifold of constant negative Gaussian curvature and of finite volume. For the motion on compact Riemann surfaces we find that a consistent formulation is only possible if the magnetic flux is quantized, as it is proportional to the (integrated) first Chern class of a certain complex line bundle over the manifold. In the case of non-compact surfaces of finite volume we obtain the striking result that the magnetic flux has to vanish identically due to the theorem that any holomorphic line bundle over a non-compact Riemann surface is holomorphically trivial. (orig.)
K-theory for discrete subgroups of the Lorentz groups
International Nuclear Information System (INIS)
Schwalbe, D.A.
1986-01-01
In the thesis, a conjecture on the structure of the topological K theory groups associated to an action of a discrete group on a manifold is verified in the special case when the group is a closed discrete subgroup of a Lorentz group. The K theory is the topological K theory of the reduced crossed product C algebra arising from the action of a countable discrete group acting by diffeomorphisms on a smooth, Hausdorf, and second and countable manifold. The proof uses the geometric K theory of Baum and Connes. In this situation, they have developed a geometrically realized K theory which they conjecture to be isomorphic to the analytic K theory. Work of Kasparov is used to show the geometric K groups and the analytic K groups are isomorphic for actions of the Lorentz groups on a manifold. Work of Marc Rieffel on Morita equivalence of C/sup */ algebras, shows the analytic K theory for a closed discrete subgroup of a Lie group acting on a manifold is isomorphic to the K theory of the Lie group itself, acting on an induced manifold
Riemann surfaces with boundaries and string theory
International Nuclear Information System (INIS)
Morozov, A.Yu.; Roslyj, A.A.
1989-01-01
A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned
The Riemann-Lovelock Curvature Tensor
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D
Exploring the Riemann zeta function 190 years from Riemann's birth
Nikeghbali, Ashkan; Rassias, Michael
2017-01-01
This book is concerned with the Riemann Zeta Function, its generalizations, and various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis and Probability Theory. Eminent experts in the field illustrate both old and new results towards the solution of long-standing problems and include key historical remarks. Offering a unified, self-contained treatment of broad and deep areas of research, this book will be an excellent tool for researchers and graduate students working in Mathematics, Mathematical Physics, Engineering and Cryptography.
Threshold analyses and Lorentz violation
International Nuclear Information System (INIS)
Lehnert, Ralf
2003-01-01
In the context of threshold investigations of Lorentz violation, we discuss the fundamental principle of coordinate independence, the role of an effective dynamical framework, and the conditions of positivity and causality. Our analysis excludes a variety of previously considered Lorentz-breaking parameters and opens an avenue for viable dispersion-relation investigations of Lorentz violation
Functionals of finite Riemann surfaces
Schiffer, Menahem
1954-01-01
This advanced monograph on finite Riemann surfaces, based on the authors' 1949-50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of ""a plethora of ideas, each interesting in its own right,"" noting that ""the patient reader will be richly rewarded."" Suitable for graduate-level courses, the text begins with three chapters that offer a development of the classical theory along historical lines, examining geometrical and physical considerations, existence theo
Quantization of a symplectic manifold associated to a manifold with projective structure
International Nuclear Information System (INIS)
Biswas, Indranil
2009-01-01
Let X be a complex manifold equipped with a projective structure P. There is a holomorphic principal C*-bundle L P ' over X associated with P. We show that the holomorphic cotangent bundle of the total space of L P ' equipped with the Liouville symplectic form has a canonical deformation quantization. This generalizes the construction in the work of and Ben-Zvi and Biswas [''A quantization on Riemann surfaces with projective structure,'' Lett. Math. Phys. 54, 73 (2000)] done under the assumption that dim C X=1.
Graded manifolds and supermanifolds
International Nuclear Information System (INIS)
Batchelor, M.
1984-01-01
In this paper, a review is presented on graded manifolds and supermanifolds. Many theorems, propositions, corrollaries, etc. are given with proofs or sketch proofs. Graded manifolds, supereuclidian space, Lie supergroups, etc. are dealt with
Pilca, Mihaela
2016-09-01
Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kähler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kähler quotient is toric.
A Polyakov action on Riemann surfaces
International Nuclear Information System (INIS)
Zucchini, R.
1991-02-01
A calculation of the effective action for induced conformal gravity on higher genus Riemann surfaces is presented. Our expression, generalizing Polyakov's formula, depends holomorphically on the Beltrami and integrates the diffeomorphism anomaly. A solution of the conformal Ward identity on an arbitrary compact Riemann surfaces without boundary is presented, and its remarkable properties are studied. (K.A.) 16 refs., 2 figs
The Riemann-Lovelock curvature tensor
International Nuclear Information System (INIS)
Kastor, David
2012-01-01
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are 'Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature. (paper)
Renteln, Paul
2013-11-01
Preface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
Lorentz violation naturalness revisited
Energy Technology Data Exchange (ETDEWEB)
Belenchia, Alessio; Gambassi, Andrea; Liberati, Stefano [SISSA - International School for Advanced Studies, via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste, via Valerio 2, 34127 Trieste (Italy)
2016-06-08
We revisit here the naturalness problem of Lorentz invariance violations on a simple toy model of a scalar field coupled to a fermion field via a Yukawa interaction. We first review some well-known results concerning the low-energy percolation of Lorentz violation from high energies, presenting some details of the analysis not explicitly discussed in the literature and discussing some previously unnoticed subtleties. We then show how a separation between the scale of validity of the effective field theory and that one of Lorentz invariance violations can hinder this low-energy percolation. While such protection mechanism was previously considered in the literature, we provide here a simple illustration of how it works and of its general features. Finally, we consider a case in which dissipation is present, showing that the dissipative behaviour does not percolate generically to lower mass dimension operators albeit dispersion does. Moreover, we show that a scale separation can protect from unsuppressed low-energy percolation also in this case.
Directory of Open Access Journals (Sweden)
José Manuel Sánchez Muñoz
2011-10-01
Full Text Available En el mes de noviembre de 1859, durante la presentación mensual de losinformes de la Academia de Berlín, el alemán Bernhard Riemann presentóun trabajo que cambiaría los designios futuros de la ciencia matemática. El tema central de su informe se centraba en los números primos, presentando el que hoy día, una vez demostrada la Conjetura de Poincaré, puede ser considerado el problema matemático abierto más importante. El presente artículo muestra en su tercera sección una traducción al castellano de dicho trabajo.
Conformal algebra of Riemann surfaces
International Nuclear Information System (INIS)
Vafa, C.
1988-01-01
It has become clear over the last few years that 2-dimensional conformal field theories are a crucial ingredient of string theory. Conformal field theories correspond to vacuum solutions of strings; or more precisely we know how to compute string spectrum and scattering amplitudes by starting from a formal theory (with a proper value of central charge of the Virasoro algebra). Certain non-linear sigma models do give rise to conformal theories. A lot of progress has been made in the understanding of conformal theories. The author discusses a different view of conformal theories which was motivated by the development of operator formalism on Riemann surfaces. The author discusses an interesting recent work from this point of view
On hyperbolic U4 manifolds with local duality
International Nuclear Information System (INIS)
Wallner, R.P.
1982-01-01
We use the decomposition of the Riemann/Cartan curvature 2-forms Ωsup(ij) in terms of their irreducible parts under the Lorentz group to examine the irreducible content of self- and anti-self double dual curvature forms Ωsup(+-ij) and their further refinements involving left and right duals. In the case of local duality (i.e. Ωsup(ij) = Ωsup(+-ij) locally), some consequences to curvature and torsion are easily derived in this way. As Riemann/Cartan space-times (U 4 -space-times) are subject to generalized gravity theories, some (vacuum) field equations proposed there are also taken into considerations. As an application to the various decompositions of curvature and torsion we point out their utility in the search of exact solutions of U 4 -field equations. To simplify notations and calculations, the calculus of exterior forms is used throughout. (Author)
Super differential forms on super Riemann surfaces
International Nuclear Information System (INIS)
Konisi, Gaku; Takahasi, Wataru; Saito, Takesi.
1994-01-01
Line integral on the super Riemann surface is discussed. A 'super differential operator' which possesses both properties of differential and of differential operator is proposed. With this 'super differential operator' a new theory of differential form on the super Riemann surface is constructed. We call 'the new differentials on the super Riemann surface' 'the super differentials'. As the applications of our theory, the existency theorems of singular 'super differentials' such as 'super abelian differentials of the 3rd kind' and of a super projective connection are examined. (author)
Three questions on Lorentz violation
Energy Technology Data Exchange (ETDEWEB)
Iorio, Alfredo [Institute of Particle and Nuclear Physics, Charles University of Prague - V Holesovickach 2, 180 00 Prague 8 (Czech Republic); Department of Physics ' E. R. Caianiello' , University of Salerno and I.N.F.N. Naples, Gruppo Collegato di Salerno - Via Allende, 84081 Baronissi (Italy)
2007-05-15
We review the basics of the two most widely used approaches to Lorentz violation - the Standard Model Extension and Noncommutative Field Theory - and discuss in some detail the example of the modified spectrum of the synchrotron radiation. Motivated by touching upon such a fundamental issue as Lorentz symmetry, we ask three questions: What is behind the search for Lorentz violation? Is String Theory a physical theory? Is there an alternative to Supersymmetry?.
Introduction to differentiable manifolds
Auslander, Louis
2009-01-01
The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff
Başkal, Sibel
2015-11-01
This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.
Kalka, Morris; Patrizio, Giorgio
2014-01-01
We study the geometric properties of complex manifolds possessing a pair of plurisubharmonic functions satisfying Monge-Amp\\`ere type of condition. The results are applied to characterize complex manifolds biholomorphic to $\\C^{N}$ viewed as a product of lower dimensional complex euclidean spaces.
Lectures on the Riemann zeta function
Iwaniec, H
2014-01-01
The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. Th...
Astroparticle tests of Lorentz symmetry
Energy Technology Data Exchange (ETDEWEB)
Diaz, Jorge [Karlsruhe Institute of Technology, Karlsruhe (Germany)
2016-07-01
Lorentz symmetry is a cornerstone of modern physics. As the spacetime symmetry of special relativity, Lorentz invariance is a basic component of the standard model of particle physics and general relativity, which to date constitute our most successful descriptions of nature. Deviations from exact symmetry would radically change our view of the universe and current experiments allow us to test the validity of this assumption. In this talk, I describe effects of Lorentz violation in cosmic rays and gamma rays that can be studied in current observatories.
Ensemble manifold regularization.
Geng, Bo; Tao, Dacheng; Xu, Chao; Yang, Linjun; Hua, Xian-Sheng
2012-06-01
We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning (SSL) problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, cross validation is applied, but it does not necessarily scale up. Other problems derive from the suboptimality incurred by discrete grid search and the overfitting. Therefore, we develop an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR carefully so it 1) learns both the composite manifold and the semi-supervised learner jointly, 2) is fully automatic for learning the intrinsic manifold hyperparameters implicitly, 3) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption, and 4) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Furthermore, we prove the convergence property of EMR to the deterministic matrix at rate root-n. Extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework.
Constraining spacetime nonmetricity with Lorentz-violation methods
Xiao, Zhi; Lehnert, Ralf; Snow, W. M.; Xu, Rui
2018-01-01
In this report, we will give the first constraints on in-matter nonmetricity. We will show how the effective-field-theory (EFT) toolbox developed for the study of Lorentz violation (LV) can be employed for investigations of the “effective LV” background caused by nonmetricity, a geometric object extending the notion of a Riemannian manifold. The idea is to probe for the effects of spacetime nonmetricity sourced by liquid 4He with polarized slow neutrons. We present the first constraints on isotropic and parity-odd nonmetricity components. Further constraints on anisotropic nonmetricity components within this EFT framework may be feasible with proper experimental techniques in the near future.
Brane Lorentz symmetry from Lorentz breaking in the bulk
Energy Technology Data Exchange (ETDEWEB)
Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Carvalho, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal)
2007-05-15
We propose the mechanism of spontaneous symmetry breaking of a bulk vector field as a way to generate the selection of bulk dimensions invisible to the standard model confined to the brane. By assigning a nonvanishing vacuum value to the vector field, a direction is singled out in the bulk vacuum, thus breaking the bulk Lorentz symmetry. We present the condition for induced Lorentz symmetry on the brane, as phenomenologically required.
Quantum Hall effect on Riemann surfaces
Tejero Prieto, Carlos
2009-06-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Quantum Hall effect on Riemann surfaces
International Nuclear Information System (INIS)
Tejero Prieto, Carlos
2009-01-01
We study the family of Landau Hamiltonians compatible with a magnetic field on a Riemann surface S by means of Fourier-Mukai and Nahm transforms. Starting from the geometric formulation of adiabatic charge transport on Riemann surfaces, we prove that Hall conductivity is proportional to the intersection product on the first homology group of S and therefore it is quantized. Finally, by using the theory of determinant bundles developed by Bismut, Gillet and Soul, we compute the adiabatic curvature of the spectral bundles defined by the holomorphic Landau levels. We prove that it is given by the polarization of the jacobian variety of the Riemann surface, plus a term depending on the relative analytic torsion.
Lorentz Covariance of Langevin Equation
International Nuclear Information System (INIS)
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
International Nuclear Information System (INIS)
Aspinwall, P.S.; Luetken, C.A.
1991-01-01
We analyze the mirror manifold hypothesis in one and three dimensions using the simplest available representations of the N = 2 superconformal algebra. The symmetries of these tensor models can be divided out to give an explicit representation of the mirror, and we give a simple group theoretical algorithm for determining which symmetries should be used. We show that the mirror of a superconformal field theory does not always have a geometrical interpretation, but when it does, deformations of complex structure of one manifold are reflected in deformations of the Kaehler form of the mirror manifold, and we show how the large radius limit of a manifold corresponds to a large complex structure limit in the mirror manifold. The mirror of the Tian-Yau three generation model is constructed both as a conformal field theory and as an algebraic variety with Euler number six. The Hodge numbers of this manifolds are fixed, but the intersection numbes are highly ambiguous, presumably reflected a rich structure of multicritical points in the moduli space of the field theory. (orig.)
Contravariant gravity on Poisson manifolds and Einstein gravity
International Nuclear Information System (INIS)
Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi
2017-01-01
A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)
Orbifold Riemann surfaces: Teichmueller spaces and algebras of geodesic functions
Energy Technology Data Exchange (ETDEWEB)
Mazzocco, Marta [Loughborough University, Loughborough (United Kingdom); Chekhov, Leonid O [Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow (Russian Federation)
2009-12-31
A fat graph description is given for Teichmueller spaces of Riemann surfaces with holes and with Z{sub 2}- and Z{sub 3}-orbifold points (conical singularities) in the Poincare uniformization. The corresponding mapping class group transformations are presented, geodesic functions are constructed, and the Poisson structure is introduced. The resulting Poisson algebras are then quantized. In the particular cases of surfaces with n Z{sub 2}-orbifold points and with one and two holes, the respective algebras A{sub n} and D{sub n} of geodesic functions (classical and quantum) are obtained. The infinite-dimensional Poisson algebra D{sub n}, which is the semiclassical limit of the twisted q-Yangian algebra Y'{sub q}(o{sub n}) for the orthogonal Lie algebra o{sub n}, is associated with the algebra of geodesic functions on an annulus with n Z{sub 2}-orbifold points, and the braid group action on this algebra is found. From this result the braid group actions are constructed on the finite-dimensional reductions of this algebra: the p-level reduction and the algebra D{sub n}. The central elements for these reductions are found. Also, the algebra D{sub n} is interpreted as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semisimple point. Bibliography: 36 titles.
Chiral bosonization on a Riemann surface
International Nuclear Information System (INIS)
Eguchi, Tohru; Ooguri, Hirosi
1987-01-01
We point out that the basic addition theorem of θ-functions, Fay's identity, implies an equivalence between bosons and chiral fermions on Riemann surfaces with arbitrary genus. We present a rule for a bosonized calculation of correlation functions. We also discuss ghost systems of n and (1-n) tensors and derive formulas for their chiral determinants. (orig.)
Gaussian curvature on hyperelliptic Riemann surfaces
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 2, May 2014, pp. 155–167. c Indian Academy of Sciences. Gaussian curvature on hyperelliptic Riemann surfaces. ABEL CASTORENA. Centro de Ciencias Matemáticas (Universidad Nacional Autónoma de México,. Campus Morelia) Apdo. Postal 61-3 Xangari, C.P. 58089 Morelia,.
Conformal deformation of Riemann space and torsion
International Nuclear Information System (INIS)
Pyzh, V.M.
1981-01-01
Method for investigating conformal deformations of Riemann spaces using torsion tensor, which permits to reduce the second ' order equations for Killing vectors to the system of the first order equations, is presented. The method is illustrated using conformal deformations of dimer sphere as an example. A possibility of its use when studying more complex deformations is discussed [ru
Study Paths, Riemann Surfaces, and Strebel Differentials
Buser, Peter; Semmler, Klaus-Dieter
2017-01-01
These pages aim to explain and interpret why the late Mika Seppälä, a conformal geometer, proposed to model student study behaviour using concepts from conformal geometry, such as Riemann surfaces and Strebel differentials. Over many years Mika Seppälä taught online calculus courses to students at Florida State University in the United States, as…
Hysteresis rarefaction in the Riemann problem
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel
2008-01-01
Roč. 138, - (2008), s. 1-10 ISSN 1742-6588. [International Workshop on Multi-Rate Processes and Hysteresis. Cork , 31.03.2008-05.04.2008] Institutional research plan: CEZ:AV0Z10190503 Keywords : Preisach hysteresis * Riemann problem Subject RIV: BA - General Mathematics http://iopscience.iop.org/1742-6596/138/1/012010
Generalized Riemann problem for reactive flows
International Nuclear Information System (INIS)
Ben-Artzi, M.
1989-01-01
A generalized Riemann problem is introduced for the equations of reactive non-viscous compressible flow in one space dimension. Initial data are assumed to be linearly distributed on both sides of a jump discontinuity. The resolution of the singularity is studied and the first-order variation (in time) of flow variables is given in exact form. copyright 1989 Academic Press, Inc
Toeplitz quantization of Kaehler manifolds and gl(N), N [yields] [infinity] limits
Energy Technology Data Exchange (ETDEWEB)
Bordemann, M. (Dept. of Physics, Univ. of Freiburg (Germany)); Meinrenken, E. (Dept. of Mathematics, M.I.T., Cambridge, MA (United States)); Schlichenmaier, M. (Dept. of Mathematics and Computer Science, Univ. of Mannheim (Germany))
1994-10-01
For general compact Kaehler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras gl(N), N [yields] [infinity]. (orig.)
Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
Energy Technology Data Exchange (ETDEWEB)
Schreck, M. [Indiana University, Indiana University Center for Spacetime Symmetries, Bloomington, IN (United States)
2015-05-15
In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal standard-model extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classical Lagrangians of the nonminimal SME fermion sector. (orig.)
Classical kinematics and Finsler structures for nonminimal Lorentz-violating fermions
International Nuclear Information System (INIS)
Schreck, M.
2015-01-01
In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal standard-model extension (SME). The properties of this Lagrangian are analyzed and two corresponding Finsler structures are obtained. One structure describes a scaled Euclidean geometry, whereas the other is neither a Riemann nor a Randers or Kropina structure. The results of the article provide some initial understanding of classical Lagrangians of the nonminimal SME fermion sector. (orig.)
Statistical mechanics and Lorentz violation
International Nuclear Information System (INIS)
Colladay, Don; McDonald, Patrick
2004-01-01
The theory of statistical mechanics is studied in the presence of Lorentz-violating background fields. The analysis is performed using the Standard-Model Extension (SME) together with a Jaynesian formulation of statistical inference. Conventional laws of thermodynamics are obtained in the presence of a perturbed hamiltonian that contains the Lorentz-violating terms. As an example, properties of the nonrelativistic ideal gas are calculated in detail. To lowest order in Lorentz violation, the scalar thermodynamic variables are only corrected by a rotationally invariant combination of parameters that mimics a (frame dependent) effective mass. Spin-couplings can induce a temperature-independent polarization in the classical gas that is not present in the conventional case. Precision measurements in the residual expectation values of the magnetic moment of Fermi gases in the limit of high temperature may provide interesting limits on these parameters
Manifold Regularized Reinforcement Learning.
Li, Hongliang; Liu, Derong; Wang, Ding
2018-04-01
This paper introduces a novel manifold regularized reinforcement learning scheme for continuous Markov decision processes. Smooth feature representations for value function approximation can be automatically learned using the unsupervised manifold regularization method. The learned features are data-driven, and can be adapted to the geometry of the state space. Furthermore, the scheme provides a direct basis representation extension for novel samples during policy learning and control. The performance of the proposed scheme is evaluated on two benchmark control tasks, i.e., the inverted pendulum and the energy storage problem. Simulation results illustrate the concepts of the proposed scheme and show that it can obtain excellent performance.
Analysis and algebra on differentiable manifolds a workbook for students and teachers
Gadea, P M
2001-01-01
A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Henc...
On Lovelock analogs of the Riemann tensor
Camanho, Xián O.; Dadhich, Naresh
2016-03-01
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.
Maps between Grassmann manifolds
Indian Academy of Sciences (India)
Parameswaran Sankaran Institute of Mathematical Sciences Chennai, India sankaran@imsc.res.in Indian Academy of Sciences Platinum Jubilee Meeting Hyderabad
2009-07-02
Jul 2, 2009 ... Classification of all manifolds (or maps between them) is an impossible task. The coarser, homotopical classification, is relatively easier–but only relatively! Homotopy is, roughly speaking, the study of properties of spaces and maps invariant under continuous deformations. Denote by [X, Y ] the set of all ...
International Nuclear Information System (INIS)
Lisboa, P.; Michael, C.
1982-01-01
We address the question of designing optimum discrete sets of points to represent numerically a continuous group manifold. We consider subsets which are extensions of the regular discrete subgroups. Applications to Monte Carlo simulation of SU(2) and SU(3) gauge theory are discussed. (orig.)
The KZB equations on Riemann surfaces
Felder, Giovanni
1996-01-01
In this paper, based on the author's lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan--Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at $n$ marked points are given. The covariant derivatives are expressed in terms of ``dynamical $r$-matrices'', a notion borrowed from integrable systems. The case of marked points moving on a fixed Riemann surface is studied more closely. We prove a universa...
Transport properties of stochastic Lorentz models
Beijeren, H. van
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed
Dual manifold heat pipe evaporator
Adkins, D.R.; Rawlinson, K.S.
1994-01-04
An improved evaporator section is described for a dual manifold heat pipe. Both the upper and lower manifolds can have surfaces exposed to the heat source which evaporate the working fluid. The tubes in the tube bank between the manifolds have openings in their lower extensions into the lower manifold to provide for the transport of evaporated working fluid from the lower manifold into the tubes and from there on into the upper manifold and on to the condenser portion of the heat pipe. A wick structure lining the inner walls of the evaporator tubes extends into both the upper and lower manifolds. At least some of the tubes also have overflow tubes contained within them to carry condensed working fluid from the upper manifold to pass to the lower without spilling down the inside walls of the tubes. 1 figure.
Analytic manifolds in uniform algebras
International Nuclear Information System (INIS)
Tonev, T.V.
1988-12-01
Here we extend Bear-Hile's result concerning the version of famous Bishop's theorem for one-dimensional analytic structures in two directions: for n-dimensional complex analytic manifolds, n>1, and for generalized analytic manifolds. 14 refs
Holonomy of Einstein Lorentzian manifolds
International Nuclear Information System (INIS)
Galaev, Anton S
2010-01-01
The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp. vacuum Einstein) Lorentzian manifold; the direct constructions are given. Also the holonomy algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The classification of the holonomy algebras of Lorentzian manifolds is reviewed and a complete description of the spaces of curvature tensors for these holonomies is given.
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Post-Quantum Cryptography: Riemann Primitives and Chrysalis
Malloy, Ian; Hollenbeck, Dennis
2018-01-01
The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors relying on the Gauss Circle Problem within the Riemann sphere. The principle security reduction proposed by this novel cryptographic scheme applies c...
Operator bosonization on Riemann surfaces: new vertex operators
International Nuclear Information System (INIS)
Semikhatov, A.M.
1989-01-01
A new formalism is proposed for the construction of an operator theory of generalized ghost systems (bc theories of spin J) on Riemann surfaces (loop diagrams of the theory of closed strings). The operators of the bc system are expressed in terms of operators of the bosonic conformal theory on a Riemann surface. In contrast to the standard bosonization formulas, which have meaning only locally, operator Baker-Akhiezer functions, which are well defined globally on a Riemann surface of arbitrary genus, are introduced. The operator algebra of the Baker-Akhiezer functions generates explicitly the algebraic-geometric τ function and correlation functions of bc systems on Riemann surfaces
The concept of a Riemann surface
Weyl, Hermann
2009-01-01
This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment
Riemann monodromy problem and conformal field theories
International Nuclear Information System (INIS)
Blok, B.
1989-01-01
A systematic analysis of the use of the Riemann monodromy problem for determining correlators (conformal blocks) on the sphere is presented. The monodromy data is constructed in terms of the braid matrices and gives a constraint on the noninteger part of the conformal dimensions of the primary fields. To determine the conformal blocks we need to know the order of singularities. We establish a criterion which tells us when the knowledge of the conformal dimensions of primary fields suffice to determine the blocks. When zero modes of the extended algebra are present the analysis is more difficult. In this case we give a conjecture that works for the SU(2) WZW case. (orig.)
Riemann surfaces and algebraic curves a first course in Hurwitz theory
Cavalieri, Renzo
2016-01-01
Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.
Quantum field theory on higher-genus Riemann surfaces
International Nuclear Information System (INIS)
Kubo, Reijiro; Yoshii, Hisahiro; Ojima, Shuichi; Paul, S.K.
1989-07-01
Quantum field theory for b-c systems is formulated on Riemann surfaces with arbitrary genus. We make use of the formalism recently developed by Krichever and Novikov. Hamiltonian is defined properly, and the Ward-Takahashi identities are derived on higher-genus Riemann surfaces. (author)
Non-abelian bosonization in higher genus Riemann surfaces
International Nuclear Information System (INIS)
Koh, I.G.; Yu, M.
1988-01-01
We propose a generalization of the character formulas of the SU(2) Kac-Moody algebra to higher genus Riemann surfaces. With this construction, we show that the modular invariant partition funciton of the SO(4) k = 1 Wess-Zumino model is equivalent, in arbitrary genus Riemann surfaces, to that of free fermion theory. (orig.)
Collisionless analogs of Riemann S ellipsoids with halo
International Nuclear Information System (INIS)
Abramyan, M.G.
1987-01-01
A spheroidal halo ensures equilibrium of the collisionless analogs of the Riemann S ellipsoids with oscillations of the particles along the direction of their rotation. Sequences of collisionless triaxial ellipsoids begin and end with dynamically stable members of collisionless embedded spheroids. Both liquid and collisionless Riemann S ellipsoids with weak halo have properties that resemble those of bars of SB galaxies
A Riemann problem with small viscosity and dispersion
Directory of Open Access Journals (Sweden)
Kayyunnapara Thomas Joseph
2006-09-01
Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.
Getting superstring amplitudes by degenerating Riemann surfaces
International Nuclear Information System (INIS)
Matone, Marco; Volpato, Roberto
2010-01-01
We explicitly show how the chiral superstring amplitudes can be obtained through factorisation of the higher genus chiral measure induced by suitable degenerations of Riemann surfaces. This powerful tool also allows to derive, at any genera, consistency relations involving the amplitudes and the measure. A key point concerns the choice of the local coordinate at the node on degenerate Riemann surfaces that greatly simplifies the computations. As a first application, starting from recent ansaetze for the chiral measure up to genus five, we compute the chiral two-point function for massless Neveu-Schwarz states at genus two, three and four. For genus higher than three, these computations include some new corrections to the conjectural formulae appeared so far in the literature. After GSO projection, the two-point function vanishes at genus two and three, as expected from space-time supersymmetry arguments, but not at genus four. This suggests that the ansatz for the superstring measure should be corrected for genus higher than four.
Analysis, manifolds and physics
Choquet-Bruhat, Y
2000-01-01
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.
Daverman, Robert J
2007-01-01
Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve
Manifold Regularized Correlation Object Tracking
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2017-01-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped fr...
Non-dissipative electromagnetic media with two Lorentz null cones
International Nuclear Information System (INIS)
Dahl, Matias F.
2013-01-01
We study Maxwell’s equations on a 4-manifold where the electromagnetic medium is modeled by an antisymmetric (2/2 )-tensor with 21 real coefficients. In this setting the Fresnel surface is a fourth-order polynomial surface that describes the dynamical response of the medium in the geometric optics limit. For example, in an isotropic medium the Fresnel surface is a Lorentz null cone. The contribution of this paper is the pointwise description of all electromagnetic medium tensors κ with real coefficients that satisfy the following three conditions: (i)medium κ is invertible, (ii)medium κ is skewon-free, or non-dissipative, (iii)the Fresnel surface of κ is the union of two distinct Lorentz null cones. We show that there are only three classes of media with these properties and give explicit expressions in local coordinates for each class. - Highlights: ► We find two new electromagnetic media classes for which the Fresnel surface decomposes into two light cones. ► In a suitable setting we classify all electromagnetic media where this is the case. ► We find an electromagnetic medium tensor with three different signal speeds in one direction. ► The work is related to [5], which classifies all media with one light cone (in a suitable setting).
Smooth Maps of a Foliated Manifold in a Symplectic Manifold
Indian Academy of Sciences (India)
Let be a smooth manifold with a regular foliation F and a 2-form which induces closed forms on the leaves of F in the leaf topology. A smooth map f : ( M , F ) ⟶ ( N , ) in a symplectic manifold ( N , ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the ...
Lorentz covariant theory of gravitation
International Nuclear Information System (INIS)
Fagundes, H.V.
1974-12-01
An alternative method for the calculation of second order effects, like the secular shift of Mercury's perihelium is developed. This method uses the basic ideas of thirring combined with the more mathematical approach of Feyman. In the case of a static source, the treatment used is greatly simplified. Besides, Einstein-Infeld-Hoffmann's Lagrangian for a system of two particles and spin-orbit and spin-spin interactions of two particles with classical spin, ie, internal angular momentum in Moller's sense, are obtained from the Lorentz covariant theory
A study of Para-Sasakian manifold
International Nuclear Information System (INIS)
Rahman, M.S.
1995-08-01
A Para-Sasakian manifold M is viewed in the light of an almost paracontact manifold. The fundamental concepts of M in spirit to Recurrent, Ricci-recurrent, 2-Recurrent and 2-Ricci-recurrent manifolds are presented. An η-Einstein manifold modelled on P-Sasakian manifold is then treated with simplified proofs of some results. (author). 7 refs
Moment-angle manifolds, intersection of quadrics and higher dimensional contact manifolds
Barreto, Yadira; Verjovsky, Alberto
2013-01-01
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
Ice cream and orbifold Riemann-Roch
International Nuclear Information System (INIS)
Buckley, Anita; Reid, Miles; Zhou Shengtian
2013-01-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
E-string theory on Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Kim, Hee-Cheol; Vafa, Cumrun [Jefferson Physical Laboratory, Harvard University, Cambridge, MA (United States); Razamat, Shlomo S. [Physics Department, Technion, Haifa (Israel); Zafrir, Gabi [Kavli IPMU (WPI), UTIAS, the University of Tokyo, Kashiwa, Chiba (Japan)
2018-01-15
We study compactifications of the 6d E-string theory, the theory of a small E{sub 8} instanton, to four dimensions. In particular we identify N = 1 field theories in four dimensions corresponding to compactifications on arbitrary Riemann surfaces with punctures and with arbitrary non-abelian flat connections as well as fluxes for the abelian sub-groups of the E{sub 8} flavor symmetry. This sheds light on emergent symmetries in a number of 4d N = 1 SCFTs (including the 'E7 surprise' theory) as well as leads to new predictions for a large number of 4-dimensional exceptional dualities and symmetries. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Transformation optics with artificial Riemann sheets
Xu, Lin; Chen, Huanyang
2013-11-01
The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777-80 and Pendry et al 2006 Science 312 1780-2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110-12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results.
Transformation optics with artificial Riemann sheets
International Nuclear Information System (INIS)
Xu, Lin; Chen, Huanyang
2013-01-01
The two original versions of ‘invisibility’ cloaks (Leonhardt 2006 Science 312 1777–80 and Pendry et al 2006 Science 312 1780–2) show perfect cloaking but require unphysical singularities in material properties. A non-Euclidean version of cloaking (Leonhardt 2009 Science 323 110–12) was later presented to address these problems, using a very complicated non-Euclidean geometry. In this work, we combine the two original approaches to transformation optics into a more general concept: transformation optics with artificial Riemann sheets. Our method is straightforward and can be utilized to design new kinds of cloaks that can work not only in the realm of geometric optics but also using wave optics. The physics behind this design is similar to that of the conformal cloak for waves. The resonances in the interior region make the phase delay disappear and induce the cloaking effect. Numerical simulations confirm our theoretical results. (paper)
Ice cream and orbifold Riemann-Roch
Buckley, Anita; Reid, Miles; Zhou, Shengtian
2013-06-01
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of {K3} surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
From Riemann to differential geometry and relativity
Papadopoulos, Athanase; Yamada, Sumio
2017-01-01
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Diffeomorphisms of elliptic 3-manifolds
Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam
2012-01-01
This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...
Manifolds of positive scalar curvature
Energy Technology Data Exchange (ETDEWEB)
Stolz, S [Department of Mathematics, University of Notre Dame, Notre Dame (United States)
2002-08-15
This lecture gives an survey on the problem of finding a positive scalar curvature metric on a closed manifold. The Gromov-Lawson-Rosenberg conjecture and its relation to the Baum-Connes conjecture are discussed and the problem of finding a positive Ricci curvature metric on a closed manifold is explained.
Complex manifolds in relativity
International Nuclear Information System (INIS)
Flaherty, E.J. Jr.
1975-01-01
Complex manifold theory is applied to the study of certain problems in general relativity. The first half of the work is devoted to the mathematical theory of complex manifold. Then a brief review of general relativity is given. It is shown that any spacetime admits locally an almost Hermitian structure, suitably modified to be compatible with the indefinite metric of spacetime. This structure is integrable if and only if the spacetime admits two geodesic and shearfree null congruences, thus in particular if the spacetime is type D vacuum or electrified. The structure is ''half-integrable'' in a suitable sense if and only if the spacetime admits one geodesic and shearfree null congruence, thus in particular for all algebraically special vacuum spacetimes. Conditions for the modified Hermitian spacetime to be Kahlerian are presented. The most general metric for such a modified Kahlerian spacetime is found. It is shown that the type D vacuum and electrified spacetimes are conformally related to modified Kahlerian spacetimes by a generally complex conformal factor. These latter are shown to possess a very rich structure, including the existence of Killing tensors and Killing vectors. A new ''explanation'' of Newman's complex coordinate transformations is given. It is felt to be superior to previous ''explanations'' on several counts. For example, a physical interpretation in terms of a symmetry group is given. The existence of new complex coordinate transformations is established: Nt is shown that any type D vacuum spacetime is obtainable from either Schwarzschild spacetime or ''C'' spacetime by a complex coordinate transformation. Finally, some related topics are discussed and areas for future work are outlined. (Diss. Abstr. Int., B)
Lorentz violations and Euclidean signature metrics
International Nuclear Information System (INIS)
Barbero G, J. Fernando; Villasenor, Eduardo J.S.
2003-01-01
We show that the families of effective actions considered by Jacobson et al. to study Lorentz invariance violations contain a class of models that represent pure general relativity with a Euclidean signature. We also point out that some members of this family of actions preserve Lorentz invariance in a generalized sense
Lorentz violation, gravitoelectromagnetic field and Bhabha scattering
Santos, A. F.; Khanna, Faqir C.
2018-01-01
Lorentz symmetry is a fundamental symmetry in the Standard Model (SM) and in General Relativity (GR). This symmetry holds true for all models at low energies. However, at energies near the Planck scale, it is conjectured that there may be a very small violation of Lorentz symmetry. The Standard Model Extension (SME) is a quantum field theory that includes a systematic description of Lorentz symmetry violations in all sectors of particle physics and gravity. In this paper, SME is considered to study the physical process of Bhabha Scattering in the Gravitoelectromagnetism (GEM) theory. GEM is an important formalism that is valid in a suitable approximation of general relativity. A new nonminimal coupling term that violates Lorentz symmetry is used in this paper. Differential cross-section for gravitational Bhabha scattering is calculated. The Lorentz violation contributions to this GEM scattering cross-section are small and are similar in magnitude to the case of the electromagnetic field.
Interpolating and sampling sequences in finite Riemann surfaces
Ortega-Cerda, Joaquim
2007-01-01
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.
Two-dimensional time dependent Riemann solvers for neutron transport
International Nuclear Information System (INIS)
Brunner, Thomas A.; Holloway, James Paul
2005-01-01
A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem
Pluripotential theory on quaternionic manifolds
Alesker, Semyon
2012-05-01
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.
Smooth maps of a foliated manifold in a symplectic manifold
Indian Academy of Sciences (India)
Abstract. Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f : (M, F) −→ (N,σ) in a symplectic manifold (N,σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the.
The exchange algebra for Liouville theory on punctured Riemann sphere
International Nuclear Information System (INIS)
Shen Jianmin; Sheng Zhengmao
1991-11-01
We consider in this paper the classical Liouville field theory on the Riemann sphere with n punctures. In terms of the uniformization theorem of Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville fields. We find that the matrice which dominate the CEA is related to the symmetry of the Lie group SL(n) in a nontrivial manner with n>3. (author). 10 refs
Meromorphic functions and cohomology on a Riemann surface
International Nuclear Information System (INIS)
Gomez-Mont, X.
1989-01-01
The objective of this set of notes is to introduce a series of concepts of Complex Analytic Geometry on a Riemann Surface. We motivate the introduction of cohomology groups through the analysis of meromorphic functions. We finish by showing that the set of infinitesimal deformations of a Riemann surface (the tangent space to Teichmueller space) may be computed as a Cohomology group. (author). 6 refs
Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry
International Nuclear Information System (INIS)
Pan, Yiwen
2014-01-01
In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S 1 ×M 4 , which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S 3 or T 3 -fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation
An introduction to differential manifolds
Lafontaine, Jacques
2015-01-01
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergra...
Manifold Regularized Correlation Object Tracking.
Hu, Hongwei; Ma, Bo; Shen, Jianbing; Shao, Ling
2018-05-01
In this paper, we propose a manifold regularized correlation tracking method with augmented samples. To make better use of the unlabeled data and the manifold structure of the sample space, a manifold regularization-based correlation filter is introduced, which aims to assign similar labels to neighbor samples. Meanwhile, the regression model is learned by exploiting the block-circulant structure of matrices resulting from the augmented translated samples over multiple base samples cropped from both target and nontarget regions. Thus, the final classifier in our method is trained with positive, negative, and unlabeled base samples, which is a semisupervised learning framework. A block optimization strategy is further introduced to learn a manifold regularization-based correlation filter for efficient online tracking. Experiments on two public tracking data sets demonstrate the superior performance of our tracker compared with the state-of-the-art tracking approaches.
Non-Kaehler attracting manifolds
International Nuclear Information System (INIS)
Dall'Agata, Gianguido
2006-01-01
We observe that the new attractor mechanism describing IIB flux vacua for Calabi-Yau compactifications has a possible extension to the landscape of non-Kaehler vacua that emerge in heterotic compactifications with fluxes. We focus on the effective theories coming from compactifications on generalized half-flat manifolds, showing that the Minkowski 'attractor points' for 3-form fluxes are special-hermitian manifolds
Vector Fields on Product Manifolds
Kurz, Stefan
2011-01-01
This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth families of vector fields defined on the factors. Vector fields are regarded as derivations of the algebra of smooth functions.
Characteristic manifolds in relativistic hypoelasticity
Energy Technology Data Exchange (ETDEWEB)
Giambo, S [Messina Univ. (Italy). Istituto di Matematica
1978-10-02
The relativistic hypoelasticity is considered and the characteristic manifolds are determined by using the Cauchy-Kovalevski theorem for the Cauchy problem with analytic initial conditions. Taking into account that the characteristic manifold represents the image of the front-wave in the space-time, it is possible to determine the velocities of propagation. Three wave-species are obtained: material waves, longitudinal waves and transverse waves.
Moduli space of torsional manifolds
International Nuclear Information System (INIS)
Becker, Melanie; Tseng, L.-S.; Yau, S.-T.
2007-01-01
We characterize the geometric moduli of non-Kaehler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang-Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3
Noncommutative gauge theory without Lorentz violation
International Nuclear Information System (INIS)
Carlson, Carl E.; Carone, Christopher D.; Zobin, Nahum
2002-01-01
The most popular noncommutative field theories are characterized by a matrix parameter θ μν that violates Lorentz invariance. We consider the simplest algebra in which the θ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology
International Nuclear Information System (INIS)
Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA
1991-01-01
We derive a q-deformed version of the Lorentz algebra by deformating the algebra SL(2, C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified with SL q (2, C) generate SU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limit q→1 the generators are those of the classical Lorentz algebra plus an additional U(1). Thus we have a deformation of SL(2, C)xU(1). (orig.)
Constraining Lorentz Violation in Electroweak Physics
Lehnert, Ralf
2018-01-01
For practical reasons, the majority of past Lorentz tests has involved stable or quasistable particles, such as photons, neutrinos, electrons, protons, and neutrons. Similar efforts in the electroweak sector have only recently taken shape. Within this context, Lorentz-violation searches in the Standard-Model Extension’s Z-Boson sector will be discussed. It is argued that existing precision data on polarized electron-electron scattering can be employed to extract the first conservative two-sided limits on Lorentz breakdown in this sector at the level of 10-7.
Hazy spaces, tangent spaces, manifolds and groups
International Nuclear Information System (INIS)
Dodson, C.T.J.
1977-03-01
The results on hazy spaces and the developments leading to hazy manifolds and groups are summarized. Proofs have appeared elsewhere so here examples are considered and some motivation for definitions and constructions in the theorems is analyzed. It is shown that quite simple ideas, intuitively acceptable, lead to remarkable similarity with the theory of differentiable manifolds. Hazy n manifolds have tangent bundles that are hazy 2n manifolds and there are hazy manifold structures for groups. Products and submanifolds are easily constructed and in particular the hazy n-sphere manifolds as submanifolds of the standard hazy manifold Zsup(n+1)
Balsara, Dinshaw S.; Nkonga, Boniface
2017-10-01
Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The fastest way of endowing such sub-structure consists of making a multidimensional extension of the HLLI Riemann solver for hyperbolic conservation laws. Presenting such a multidimensional analogue of the HLLI Riemann solver with linear sub-structure for use on structured meshes is the goal of this work. The multidimensional MuSIC Riemann solver documented here is universal in the sense that it can be applied to any hyperbolic conservation law. The multidimensional Riemann solver is made to be consistent with constraints that emerge naturally from the Galerkin projection of the self-similar states within the wave model. When the full eigenstructure in both directions is used in the present Riemann solver, it becomes a complete Riemann solver in a multidimensional sense. I.e., all the intermediate waves are represented in the multidimensional wave model. The work also presents, for the very first time, an important analysis of the dissipation characteristics of multidimensional Riemann solvers. The present Riemann solver results in the most efficient implementation of a multidimensional Riemann solver with sub-structure. Because it preserves stationary linearly degenerate waves, it might also help with well-balancing. Implementation-related details are presented in pointwise fashion for the one-dimensional HLLI Riemann solver as well as the multidimensional MuSIC Riemann solver.
Lorentz violations in multifractal spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)
Lorentz violation. Motivation and new constraints
International Nuclear Information System (INIS)
Liberati, S.; Maccione, L.
2009-09-01
We review the main theoretical motivations and observational constraints on Planck scale sup-pressed violations of Lorentz invariance. After introducing the problems related to the phenomenological study of quantum gravitational effects, we discuss the main theoretical frameworks within which possible departures from Lorentz invariance can be described. In particular, we focus on the framework of Effective Field Theory, describing several possible ways of including Lorentz violation therein and discussing their theoretical viability. We review the main low energy effects that are expected in this framework. We discuss the current observational constraints on such a framework, focusing on those achievable through high-energy astrophysics observations. In this context we present a summary of the most recent and strongest constraints on QED with Lorentz violating non-renormalizable operators. Finally, we discuss the present status of the field and its future perspectives. (orig.)
Testing Lorentz invariance of dark matter
Blas, Diego; Sibiryakov, Sergey
2012-01-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Testing Lorentz invariance of dark matter
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Group, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Ivanov, Mikhail M.; Sibiryakov, Sergey, E-mail: diego.blas@cern.ch, E-mail: mm.ivanov@physics.msu.ru, E-mail: sibir@inr.ac.ru [Faculty of Physics, Moscow State University, Vorobjevy Gory, 119991 Moscow (Russian Federation)
2012-10-01
We study the possibility to constrain deviations from Lorentz invariance in dark matter (DM) with cosmological observations. Breaking of Lorentz invariance generically introduces new light gravitational degrees of freedom, which we represent through a dynamical timelike vector field. If DM does not obey Lorentz invariance, it couples to this vector field. We find that this coupling affects the inertial mass of small DM halos which no longer satisfy the equivalence principle. For large enough lumps of DM we identify a (chameleon) mechanism that restores the inertial mass to its standard value. As a consequence, the dynamics of gravitational clustering are modified. Two prominent effects are a scale dependent enhancement in the growth of large scale structure and a scale dependent bias between DM and baryon density perturbations. The comparison with the measured linear matter power spectrum in principle allows to bound the departure from Lorentz invariance of DM at the per cent level.
Lorentz violation. Motivation and new constraints
Energy Technology Data Exchange (ETDEWEB)
Liberati, S. [Scuola Internazionale Superiore di Studi Avanzati SISSA, Trieste (Italy); Istituto Nazionale di Fisica Nucleare INFN, Sezione di Trieste (Italy); Maccione, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2009-09-15
We review the main theoretical motivations and observational constraints on Planck scale sup-pressed violations of Lorentz invariance. After introducing the problems related to the phenomenological study of quantum gravitational effects, we discuss the main theoretical frameworks within which possible departures from Lorentz invariance can be described. In particular, we focus on the framework of Effective Field Theory, describing several possible ways of including Lorentz violation therein and discussing their theoretical viability. We review the main low energy effects that are expected in this framework. We discuss the current observational constraints on such a framework, focusing on those achievable through high-energy astrophysics observations. In this context we present a summary of the most recent and strongest constraints on QED with Lorentz violating non-renormalizable operators. Finally, we discuss the present status of the field and its future perspectives. (orig.)
Constrained Gauge Fields from Spontaneous Lorentz Violation
Chkareuli, J L; Jejelava, J G; Nielsen, H B
2008-01-01
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_{\\mu}^{2}=M^{2}$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and $CPT$) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical ...
Constrained gauge fields from spontaneous Lorentz violation
DEFF Research Database (Denmark)
Chkareuli, J. L.; Froggatt, C. D.; Jejelava, J. G.
2008-01-01
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type AµAµ=M2 (M is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant...... theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory...... couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance. Udgivelsesdato: June 11...
The Scientific Correspondence of H A Lorentz
Kox, AJ
2008-01-01
Presents a selection of more than 400 letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death.
New bounds on isotropic Lorentz violation
International Nuclear Information System (INIS)
Carone, Christopher D.; Sher, Marc; Vanderhaeghen, Marc
2006-01-01
Violations of Lorentz invariance that appear via operators of dimension four or less are completely parametrized in the Standard Model Extension (SME). In the pure photonic sector of the SME, there are 19 dimensionless, Lorentz-violating parameters. Eighteen of these have experimental upper bounds ranging between 10 -11 and 10 -32 ; the remaining parameter, k-tilde tr , is isotropic and has a much weaker bound of order 10 -4 . In this Brief Report, we point out that k-tilde tr gives a significant contribution to the anomalous magnetic moment of the electron and find a new upper bound of order 10 -8 . With reasonable assumptions, we further show that this bound may be improved to 10 -14 by considering the renormalization of other Lorentz-violating parameters that are more tightly constrained. Using similar renormalization arguments, we also estimate bounds on Lorentz-violating parameters in the pure gluonic sector of QCD
k-essence explains a Lorentz violation experiment
International Nuclear Information System (INIS)
Li Miao; Pang Yi; Wang Yi
2009-01-01
Recently, a state of the art experiment shows evidence for Lorentz violation in the gravitational sector. To explain this experiment, we investigate a spontaneous Lorentz violation scenario with a generalized scalar field. We find that when the scalar field is nonminimally coupled to gravity, the Lorentz violation induces a deformation in the Newtonian potential along the direction of Lorentz violation.
Solution of Riemann problem for ideal polytropic dusty gas
International Nuclear Information System (INIS)
Nath, Triloki; Gupta, R.K.; Singh, L.P.
2017-01-01
Highlights : • A direct approach is used to solve the Riemann problem for dusty ideal polytropic gas. • An analytical solution to the Riemann problem for dusty gas flow is obtained. • The existence and uniqueness of the solution in dusty gas is discussed. • Properties of elementary wave solutions of Riemann problem are discussed. • Effect of mass fraction of solid particles on the solution is presented. - Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.
The topology of toric origami manifolds
Holm, Tara; Pires, Ana Rita
2012-01-01
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology i...
Lorentz Transformation from Symmetry of Reference Principle
International Nuclear Information System (INIS)
Petre, M.; Dima, M.; Dima, A.; Petre, C.; Precup, I.
2010-01-01
The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.
Riemann solvers and undercompressive shocks of convex FPU chains
International Nuclear Information System (INIS)
Herrmann, Michael; Rademacher, Jens D M
2010-01-01
We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space–time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax shocks are replaced by so-called dispersive shocks. For convex–concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave–convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions
Principal Curves on Riemannian Manifolds.
Hauberg, Soren
2016-09-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.
Slow manifolds in chemical kinetics
International Nuclear Information System (INIS)
Shahzad, M.; Haq, I. U.; Sultan, F.; Wahab, A.; Faizullah, F.; Rahman, G. U.
2016-01-01
Modelling the chemical system, especially for complex and higher dimensional problems, gives an easy way to handle the ongoing reaction process with respect to time. Here, we will consider some of the newly developed computational methods commonly used for model reductions in a chemical reaction. An effective (simple) method is planned to measure the low dimensional manifold, which reduces the higher dimensional system in such a way that it may not affect the precision of the whole mechanism. The phase flow of the solution trajectories near the equilibrium point is observed while the initial approximation is measured with the spectral quasi equilibrium manifold, which starts from the equilibrium point. To make it an invariant curve, the approximated curve is first refined a certain number of times using the method of invariant grids. The other way of getting the reduced data in the low dimensional manifold is possible through the intrinsic low dimensional manifold. Then, we compare these two invariant curves given by both the methods. Finally, the idea is extended to the higher dimensional manifold, where more number of progress variables will be added. (author)
Riemann surfaces, Clifford algebras and infinite dimensional groups
International Nuclear Information System (INIS)
Carey, A.L.; Eastwood, M.G.; Hannabuss, K.C.
1990-01-01
We introduce of class of Riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional Clifford algebra. Acting by automorphisms of this algebra is a 'gauge' group of meromorphic functions on the Riemann surface. There is a natural Fock representation of the Clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of Kac-Moody algebras via a Fock representation of the Fermion algebra. In the genus one case we find a form of vertex operator construction which allows us to prove a version of the Boson-Fermion correspondence. These results are motivated by the analysis of soliton solutions of the Landau-Lifshitz equation and are rather distinct from recent developments in quantum field theory on Riemann surfaces. (orig.)
BRST quantization of superconformal theories on higher genus Riemann surfaces
International Nuclear Information System (INIS)
Leman Kuang
1992-01-01
A complex contour integral method is constructed and applied to the Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of string theories on higher genus Riemann surfaces with N=0 and 1 Krichever-Novikov (KN) algebras. This method makes calculations very simple. It is shown that the critical spacetime dimension of the string theories on a genus-g Riemann surface equals that of the string theories on a genus-zero Riemann surface, and that the 'Regge intercepts' in the genus-g case are α(g)=1-3/4g-9/8g 2 and 1/2-3/4g-17/16g 2 for bosonic strings and superstrings, respectively. (orig.)
Stein Manifolds and Holomorphic Mappings
Forstneric, Franc
2011-01-01
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. This book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applicat
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Blowup for flat slow manifolds
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall
2017-01-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a......) the regularization of piecewise smooth systems by tanh, (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b)....
Blowup for flat slow manifolds
Kristiansen, K. U.
2017-05-01
In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a) the regularization of piecewise smooth systems by \\tanh , (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b).
Matrix regularization of 4-manifolds
Trzetrzelewski, M.
2012-01-01
We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...
Connections and curvatures on complex Riemannian manifolds
International Nuclear Information System (INIS)
Ganchev, G.; Ivanov, S.
1991-05-01
Characteristic connection and characteristic holomorphic sectional curvatures are introduced on a complex Riemannian manifold (not necessarily with holomorphic metric). For the class of complex Riemannian manifolds with holomorphic characteristic connection a classification of the manifolds with (pointwise) constant holomorphic characteristic curvature is given. It is shown that the conformal geometry of complex analytic Riemannian manifolds can be naturally developed on the class of locally conformal holomorphic Riemannian manifolds. Complex Riemannian manifolds locally conformal to the complex Euclidean space are characterized with zero conformal fundamental tensor and zero conformal characteristic tensor. (author). 12 refs
Generalized graph manifolds and their effective recognition
International Nuclear Information System (INIS)
Matveev, S V
1998-01-01
A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented
Compact Riemann surfaces an introduction to contemporary mathematics
Jost, Jürgen
2006-01-01
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
The sewing technique and correlation functions on arbitrary Riemann surfaces
International Nuclear Information System (INIS)
Di Vecchia, P.
1989-01-01
We describe in the case of free bosonic and fermionic theories the sewing procedure, that is a very convenient way for constructing correlation functions of these theories on an arbitrary Riemann surface from their knowledge on the sphere. The fundamental object that results from this construction is the N-point g-loop vertex. It summarizes the information of all correlation functions of the theory on an arbitrary Riemann surface. We then check explicitly the bosonization rules and derive some useful formulas. (orig.)
Line operators from M-branes on compact Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
Amariti, Antonio [Physics Department, The City College of the CUNY, 160 Convent Avenue, New York, NY 10031 (United States); Orlando, Domenico [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Reffert, Susanne, E-mail: sreffert@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
2016-12-15
In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. The latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.
On Riemann zeroes, lognormal multiplicative chaos, and Selberg integral
International Nuclear Information System (INIS)
Ostrovsky, Dmitry
2016-01-01
Rescaled Mellin-type transforms of the exponential functional of the Bourgade–Kuan–Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot–Bacry–Muzy. The conjecture implies that a non-trivial, log-infinitely divisible probability distribution is associated with Riemann zeroes. For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic extension of the Selberg integral. (paper)
Riemann zeta function from wave-packet dynamics
DEFF Research Database (Denmark)
Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.
2010-01-01
We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
A method is proposed for classification of exactly and completely integrable embeddings of two dimensional manifoilds into Riemann or non-Riemann enveloping space, which are based on the algebraic approach to the integration of nonlinear dynamical systems.Here the grading conditions and spectral structure of the Lax-pair operators taking the values in a graded Lie algebra that pick out the integrable class of nonlinear systems are formulated 1n terms of a structure of the 3-d fundamental form tensors. Corresponding to every embedding of three-dimensional subalgebra sb(2) into a simple finite-dimensional (infinite-dimensional of finite growth) Lie algebra L is a definite class of exactly (completely) integrable embeddings of two dimensional manifold into the corresponding enveloping space supplied with the structure of L
Cayley transform on Stiefel manifolds
Macías-Virgós, Enrique; Pereira-Sáez, María José; Tanré, Daniel
2018-01-01
The Cayley transform for orthogonal groups is a well known construction with applications in real and complex analysis, linear algebra and computer science. In this work, we construct Cayley transforms on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimization problems are presented.
Principal Curves on Riemannian Manifolds
DEFF Research Database (Denmark)
Hauberg, Søren
2015-01-01
Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Eucl...
Collective coordinates on symplectic manifolds
International Nuclear Information System (INIS)
Razumov, A.V.; Taranov, A.Yu.
1981-01-01
For an arbitrary Lie group of canonical transformations on a symplectic manifold collective coordinates are introduced. They describe a motion of the dynamical system as a whole under the group transformations. Some properties of Lie group of canonical transformations are considered [ru
Obstruction theory on 8-manifolds
Czech Academy of Sciences Publication Activity Database
Čadek, M.; Crabb, M.; Vanžura, Jiří
2008-01-01
Roč. 127, č. 2 (2008), s. 167-186 ISSN 0025-2611 R&D Projects: GA ČR GA201/05/2117 Institutional research plan: CEZ:AV0Z10190503 Keywords : 8-manifolds * obstruction theory Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2008
An imbedding of Lorentzian manifolds
International Nuclear Information System (INIS)
Kim, Do-Hyung
2009-01-01
A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.
Integrability of Liouville system on high genus Riemann surface: Pt. 1
International Nuclear Information System (INIS)
Chen Yixin; Gao Hongbo
1992-01-01
By using the theory of uniformization of Riemann-surfaces, we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface
Indian Academy of Sciences (India)
Abstract. This paper is concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kähler–Norden manifolds using the theory of Tachibana operators is presented.
Rank Two Affine Manifolds in Genus 3
Aulicino, David; Nguyen, Duc-Manh
2016-01-01
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.
Lorentz violation and black-hole thermodynamics
International Nuclear Information System (INIS)
Betschart, G.; Kant, E.; Klinkhamer, F.R.
2009-01-01
We consider nonstandard photons from nonbirefringent modified Maxwell theory and discuss their propagation in a fixed Schwarzschild spacetime background. This particular modification of Maxwell theory is Lorentz-violating and allows for maximal photon velocities differing from the causal speed c of the asymptotic background spacetime. In the limit of geometrical optics, light rays from modified Maxwell theory are found to propagate along null geodesics in an effective metric. We observe that not every Lorentz-violating theory with multiple maximal velocities different from the causal speed c modifies the notion of the event horizon, contrary to naive expectations. This result implies that not every Lorentz-violating theory with multiple maximal velocities necessarily leads to a contradiction with the generalized second law of thermodynamics.
Improved test of Lorentz invariance in electrodynamics
International Nuclear Information System (INIS)
Wolf, Peter; Bize, Sebastien; Clairon, Andre; Santarelli, Giorgio; Tobar, Michael E.; Luiten, Andre N.
2004-01-01
We report new results of a test of Lorentz invariance based on the comparison of a cryogenic sapphire microwave resonator and a hydrogen-maser. The experimental results are shown together with an extensive analysis of systematic effects. Previously, this experiment has set the most stringent constraint on Kennedy-Thorndike type violations of Lorentz invariance. In this work we present new data and interpret our results in the general Lorentz violating extension of the standard model of particle physics (SME). Within the photon sector of the SME, our experiment is sensitive to seven SME parameters. We marginally improve present limits on four of these, and by a factor seven to ten on the other three
Spontaneous Lorentz breaking at high energies
International Nuclear Information System (INIS)
Cheng, H.-C.; Luty, Markus A.; Mukohyama, Shinji; Thaler, Jesse
2006-01-01
Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model ('ghost condensation') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ∼ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. We show that nonlinear effects become important for gravitational fields with strength Φ 1/2 ∼> g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M ∼ 12 GeV, g 2 10 15 GeV). If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models
Einstein-Yang-Mills-Lorentz black holes
Energy Technology Data Exchange (ETDEWEB)
Cembranos, Jose A.R.; Gigante Valcarcel, Jorge [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-12-15
Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows one to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories. (orig.)
The Lorentz integral transform and its inversion
International Nuclear Information System (INIS)
Barnea, N.; Efros, V.D.; Leidemann, W.; Orlandini, G.
2010-01-01
The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due to a historical misconception. In this connection standard regularization procedures for the solution of the integral transform problem are presented. In particular a recent one is considered in detail and critical comments on it are provided. In addition a general remark concerning the concept of the Lorentz integral transform as a method with a controlled resolution is made. (author)
Vortices in superconductors from Lorentz violation
International Nuclear Information System (INIS)
Belich, H.; Orlando, M.T.D.; Costa-Soares, T.; Helayel-Neto, J.A.
2004-01-01
We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions, and carry out its dimensional reduction to D = 1 + 2. The planar model resulting thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background, v μ ) that realizes Lorentz violation for the reduced model. Vortex type solutions of the planar model are investigated in a superconducting environment . Our vortex solutions are electrically charged and exhibit a screened electric field. (author)
Nonlinear Lorentz-invariant theory of gravitation
International Nuclear Information System (INIS)
Petry, W.
1976-01-01
A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)
Self-duality in generalized Lorentz superspaces
International Nuclear Information System (INIS)
Devchand, C.; Nuyts, J.
1996-12-01
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspace are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures. (author). 4 refs
On an isospectrality question over compact Riemann surfaces
International Nuclear Information System (INIS)
Srinivas Rau, S.
1990-01-01
It is proved that for a generic compact Riemann surface X of genus g>1,(i) there are at most 2 2g unitary characters of π 1 (X) whose associated line bundles have laplacians of identical spectrum, (ii) generating cycles for π 1 (X) can be chosen to be closed geodesics whose length multiplicity is 1. (author). 5 refs
Colliding holes in Riemann surfaces and quantum cluster algebras
Chekhov, Leonid; Mazzocco, Marta
2018-01-01
In this paper, we describe a new type of surgery for non-compact Riemann surfaces that naturally appears when colliding two holes or two sides of the same hole in an orientable Riemann surface with boundary (and possibly orbifold points). As a result of this surgery, bordered cusps appear on the boundary components of the Riemann surface. In Poincaré uniformization, these bordered cusps correspond to ideal triangles in the fundamental domain. We introduce the notion of bordered cusped Teichmüller space and endow it with a Poisson structure, quantization of which is achieved with a canonical quantum ordering. We give a complete combinatorial description of the bordered cusped Teichmüller space by introducing the notion of maximal cusped lamination, a lamination consisting of geodesic arcs between bordered cusps and closed geodesics homotopic to the boundaries such that it triangulates the Riemann surface. We show that each bordered cusp carries a natural decoration, i.e. a choice of a horocycle, so that the lengths of the arcs in the maximal cusped lamination are defined as λ-lengths in Thurston-Penner terminology. We compute the Goldman bracket explicitly in terms of these λ-lengths and show that the groupoid of flip morphisms acts as a generalized cluster algebra mutation. From the physical point of view, our construction provides an explicit coordinatization of moduli spaces of open/closed string worldsheets and their quantization.
Weyl transforms associated with the Riemann-Liouville operator
Directory of Open Access Journals (Sweden)
N. B. Hamadi
2006-01-01
Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.
Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2007-01-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established
Toeplitz operators on higher Cauchy-Riemann spaces
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Zhang, G.
2017-01-01
Roč. 22, č. 22 (2017), s. 1081-1116 ISSN 1431-0643 Institutional support: RVO:67985840 Keywords : Toeplitz operator * Hankel operator * Cauchy-Riemann operators Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 0.800, year: 2016 https://www. math .uni-bielefeld.de/documenta/vol-22/32.html
The beauty of the Riemann-Silberstein vector
International Nuclear Information System (INIS)
Bialynicki-Birula, I.
2005-01-01
Beams of light carrying angular momentum have recently been widely studied theoretically and experimentally. In my talk I will show that the description of these beams in terms of the Riemann-Silberstein vector offers many advantages. In particular, it provides a natural bridge between the classical and the quantum description. (author)
Constructions of Calabi-Yau manifolds
International Nuclear Information System (INIS)
Hubsch, T.
1987-01-01
Among possible compactifications of Superstring Theories (defined in 9+1 dimensional space-time) it is argued that only those in Calabi-Yau manifolds may lead to phenomenologically acceptable models. Thus, constructions of such manifolds are studied and a huge sequence is presented, giving rise to many possibly applicable manifolds
Natural Connections on Riemannian Product Manifolds
Gribacheva, Dobrinka
2011-01-01
A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.
A viewpoint on nearly conformally symmetric manifold
International Nuclear Information System (INIS)
Rahman, M.S.
1990-06-01
Some observations, with definition, on Nearly Conformally Symmetric (NCS) manifold are made. A number of theorems concerning conformal change of metric and parallel tensors on NCS manifolds are presented. It is illustrated that a manifold M = R n-1 x R + 1 , endowed with a special metric, is NCS but not of harmonic curvature. (author). 8 refs
Lorentz-violating electrodynamics and the cosmic microwave background.
Kostelecký, V Alan; Mewes, Matthew
2007-07-06
Possible Lorentz-violating effects in the cosmic microwave background are studied. We provide a systematic classification of renormalizable and nonrenormalizable operators for Lorentz violation in electrodynamics and use polarimetric observations to search for the associated violations.
Lorentz covariant canonical symplectic algorithms for dynamics of charged particles
Wang, Yulei; Liu, Jian; Qin, Hong
2016-12-01
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz covariance, a general procedure for constructing Lorentz covariant canonical symplectic algorithms (LCCSAs) is provided, based on which an explicit LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses Lorentz invariance as well as long-term numerical accuracy and stability, due to the preservation of a discrete symplectic structure and the Lorentz symmetry of the system. For situations with time-dependent electromagnetic fields, which are difficult to handle in traditional construction procedures of symplectic algorithms, LCCSA provides a perfect explicit canonical symplectic solution by implementing the discretization in 4-spacetime. We also show that LCCSA has built-in energy-based adaptive time steps, which can optimize the computation performance when the Lorentz factor varies.
Test of CPT and Lorentz invariance from muonium spectroscopy
Hughes, V. W.; Perdekamp, M. Grosse; Kawall, D.; Liu, W.; Jungmann, K.; Putlitz, G. zu
2001-01-01
Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts $\\delta\
Flexible fuel cell gas manifold system
Cramer, Michael; Shah, Jagdish; Hayes, Richard P.; Kelley, Dana A.
2005-05-03
A fuel cell stack manifold system in which a flexible manifold body includes a pan having a central area, sidewall extending outward from the periphery of the central area, and at least one compound fold comprising a central area fold connecting adjacent portions of the central area and extending between opposite sides of the central area, and a sidewall fold connecting adjacent portions of the sidewall. The manifold system further includes a rail assembly for attachment to the manifold body and adapted to receive pins by which dielectric insulators are joined to the manifold assembly.
Classroom Experiment to Verify the Lorentz Force
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 3. Classroom Experiment to Verify the Lorentz Force. Somnath Basu Anindita Bose Sumit Kumar Sinha Pankaj Vishe S Chatterjee. Classroom Volume 8 Issue 3 March 2003 pp 81-86 ...
Spacetime-varying couplings and Lorentz violation
International Nuclear Information System (INIS)
Kostelecky, V. Alan; Lehnert, Ralf; Perry, Malcolm J.
2003-01-01
Spacetime-varying coupling constants can be associated with violations of local Lorentz invariance and CPT symmetry. An analytical supergravity cosmology with a time-varying fine-structure constant provides an explicit example. Estimates are made for some experimental constraints
Lorentz Spengler's descriptions of chitons (Mollusca: Polyplacophora)
Kaas, P.; Knudsen, J.
1992-01-01
The present paper deals with an important Danish paper on the Polyplacophora, published in 1797 by Lorentz Spengler: Udförlig Beskrivelse over det mangeskallede Konkylie-Slaegt, af Linnaeus kaldet Chiton; med endeel nye Arter og Varieteter. -Skrivter af Naturhistorie-Selskabet, 4e Bind, Ie Hefte,
Characterisation of Embeddings in Lorentz Spaces
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Johansson, M.; Okpoti, C.A.; Persson, L. E.
2007-01-01
Roč. 76, č. 1 (2007), s. 69-92 ISSN 0004-9727 R&D Projects: GA ČR GA201/05/2033 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-increasing rearrangement * Lorentz spaces * weights Subject RIV: BA - General Mathematics Impact factor: 0.297, year: 2007
Minimal Webs in Riemannian Manifolds
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-01-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Invariance for Single Curved Manifold
Castro, Pedro Machado Manhaes de
2012-08-01
Recently, it has been shown that, for Lambert illumination model, solely scenes composed by developable objects with a very particular albedo distribution produce an (2D) image with isolines that are (almost) invariant to light direction change. In this work, we provide and investigate a more general framework, and we show that, in general, the requirement for such in variances is quite strong, and is related to the differential geometry of the objects. More precisely, it is proved that single curved manifolds, i.e., manifolds such that at each point there is at most one principal curvature direction, produce invariant is surfaces for a certain relevant family of energy functions. In the three-dimensional case, the associated energy function corresponds to the classical Lambert illumination model with albedo. This result is also extended for finite-dimensional scenes composed by single curved objects. © 2012 IEEE.
Torsions of 3-dimensional manifolds
Wurzbacher, T
2002-01-01
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." ―Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. …Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." ―Mathematical Reviews
Manifold seal structure for fuel cell stack
Collins, William P.
1988-01-01
The seal between the sides of a fuel cell stack and the gas manifolds is improved by adding a mechanical interlock between the adhesive sealing strip and the abutting surface of the manifolds. The adhesive is a material which can flow to some extent when under compression, and the mechanical interlock is formed providing small openings in the portion of the manifold which abuts the adhesive strip. When the manifolds are pressed against the adhesive strips, the latter will flow into and through the manifold openings to form buttons or ribs which mechanically interlock with the manifolds. These buttons or ribs increase the bond between the manifolds and adhesive, which previously relied solely on the adhesive nature of the adhesive.
The Lorentz Theory of Electrons and Einstein's Theory of Relativity
Goldberg, Stanley
1969-01-01
Traces the development of Lorentz's theory of electrons as applied to the problem of the electrodynamics of moving bodies. Presents evidence that the principle of relativity did not play an important role in Lorentz's theory, and that though Lorentz eventually acknowledged Einstein's work, he was unwilling to completely embrace the Einstein…
Anomalies, conformal manifolds, and spheres
Energy Technology Data Exchange (ETDEWEB)
Gomis, Jaume [Perimeter Institute for Theoretical Physics,Waterloo, Ontario, N2L 2Y5 (Canada); Hsin, Po-Shen [Department of Physics, Princeton University,Princeton, NJ 08544 (United States); Komargodski, Zohar; Schwimmer, Adam [Weizmann Institute of Science,Rehovot 76100 (Israel); Seiberg, Nathan [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,14476 Golm (Germany)
2016-03-04
The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space M is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail N=(2,2) and N=(0,2) supersymmetric theories in d=2 and N=2 supersymmetric theories in d=4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For N=(2,2) theories in d=2 and N=2 theories in d=4 we also show that the relation between the sphere partition function and the Kähler potential of M follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.
Yamazaki, Masahito
2012-05-01
We study 4d superconformal indices for a large class of {N} = 1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T 2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T 2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in {{H}^3} , each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph. The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results [1].
BPS Lorentz-violating vortex solutions
International Nuclear Information System (INIS)
Casana, Rodolfo; Ferreira Junior, Manoel M.; Hora, E. da
2011-01-01
In this work, we deal with the construction of static Bogomol'nyi-Prasad-Sommerfield (BPS) rotationally symmetric configurations on the dimensional CPT-even Lorentz-breaking photonic sector of the Standard Model Extension (SME). The main objective of this presentation is to show the possibility of obtaining such BPS solutions, even in the presence of a Lorentz-violating background. A secondary objective is to analyze the effects of this background on such topologically non-trivial BPS configurations. In order to obtain these results, we deal with some specific components of Lorentz-violating field, handling with the static Euler-Lagrange equation of motion to gauge field, from which we fix temporal gauge (absence of electric field) as a proper gauge choice. Also, considering this equation, we consistently determine an interesting configuration (discarding non-interesting ones) to the Lorentz-breaking sector. Using this configuration and the standard rotationally symmetric vortex Ansatz (which describes the behaviors of Higgs and gauge fields via two profile functions, g(r) and a(r), respectively), we construct a rotationally symmetric expression to the energy density of the system. To obtain BPS solutions, we rewrite this expression in order to have static vortex solutions satisfying a set of first order differential equations (BPS ones). The existence of such solutions is strongly constrained by a relation between some parameters of the model, including the Lorentz-breaking one. Naturally, we show that the total energy of these BPS solutions is proportional to their magnetic flux, which is quantized according to their winding number. Using suitable boundary conditions (near the origin and asymptotically), we numerically integrate the BPS equations (by means of the shooting method). By this way, we obtain solutions for some physical quantities (Higgs field, magnetic field and energy density) for several values of the Lorentz-violating parameters. From these
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Riemann-Theta Boltzmann Machine arXiv
Krefl, Daniel; Haghighat, Babak; Kahlen, Jens
A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given visible states can also be calculated analytically, yielding a derivative of the logarithmic Riemann-Theta function. The conditional expectation can be used as activation function in a feedforward neural network, thereby increasing the modelling capacity of the network. Both the Boltzmann machine and the derived feedforward neural network can be successfully trained via standard gradient- and non-gradient-based optimization techniques.
Exploration and extension of an improved Riemann track fitting algorithm
Strandlie, A.; Frühwirth, R.
2017-09-01
Recently, a new Riemann track fit which operates on translated and scaled measurements has been proposed. This study shows that the new Riemann fit is virtually as precise as popular approaches such as the Kalman filter or an iterative non-linear track fitting procedure, and significantly more precise than other, non-iterative circular track fitting approaches over a large range of measurement uncertainties. The fit is then extended in two directions: first, the measurements are allowed to lie on plane sensors of arbitrary orientation; second, the full error propagation from the measurements to the estimated circle parameters is computed. The covariance matrix of the estimated track parameters can therefore be computed without recourse to asymptotic properties, and is consequently valid for any number of observation. It does, however, assume normally distributed measurement errors. The calculations are validated on a simulated track sample and show excellent agreement with the theoretical expectations.
Pseudo-periodic maps and degeneration of Riemann surfaces
Matsumoto, Yukio
2011-01-01
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Extended Riemann-Liouville type fractional derivative operator with applications
Directory of Open Access Journals (Sweden)
Agarwal P.
2017-12-01
Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
Quantum field theory on higher-genus Riemann surfaces, 2
International Nuclear Information System (INIS)
Kubo, Reijiro; Ojima, Shuichi.
1990-08-01
Quantum field theory for closed bosonic string systems is formulated on arbitrary higher-genus Riemann surfaces in global operator formalism. Canonical commutation relations between bosonic string field X μ and their conjugate momenta P ν are derived in the framework of conventional quantum field theory. Problems arising in quantizing bosonic systems are considered in detail. Applying the method exploited in the preceding paper we calculate Ward-Takahashi identities. (author)
A contribution to the great Riemann solver debate
Quirk, James J.
1992-01-01
The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
Submaximal Riemann-Roch expected curves and symplectic packing.
Directory of Open Access Journals (Sweden)
Wioletta Syzdek
2007-06-01
Full Text Available We study Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ in the context of the Nagata-Biran conjecture. This conjecture predicts that for sufficiently large number of points multiple points Seshadri constants of an ample line bundle on algebraic surface are maximal. Biran gives an effective lower bound $N_0$. We construct examples verifying to the effect that the assertions of the Nagata-Biran conjecture can not hold for small number of points. We discuss cases where our construction fails. We observe also that there exists a strong relation between Riemann-Roch expected curves on $mathbb{P}^1 imes mathbb{P}^1$ and the symplectic packing problem. Biran relates the packing problem to the existence of solutions of certain Diophantine equations. We construct such solutions for any ample line bundle on $mathbb{P}^1 imes mathbb{P}^1$ and a relatively smallnumber of points. The solutions geometrically correspond to Riemann-Roch expected curves. Finally we discuss in how far the Biran number $N_0$ is optimal in the case of mathbb{P}^1 imes mathbb{P}^1. In fact we conjecture that it can be replaced by a lower number and we provide evidence justifying this conjecture.
Conformal scalar fields and chiral splitting on super Riemann surfaces
International Nuclear Information System (INIS)
D'Hoker, E.; Phong, D.H.
1989-01-01
We provide a complete description of correlation functions of scalar superfields on a super Riemann surface, taking into account zero modes and non-trivial topology. They are built out of chirally split correlation functions, or conformal blocks at fixed internal momenta. We formulate effective rules which determine these completely in terms of geometric invariants of the super Riemann surface. The chirally split correlation functions have non-trivial monodromy and produce single-valued amplitudes only upon integration over loop momenta. Our discussion covers the even spin structure as well as the odd spin structure case which had been the source of many difficulties in the past. Super analogues of Green's functions, holomorphic spinors, and prime forms emerge which should pave the way to function theory on super Riemann surfaces. In superstring theories, chirally split amplitudes for scalar superfields are crucial in enforcing the GSO projection required for consistency. However one really knew how to carry this out only in the operator formalism to one-loop order. Our results provide a way of enforcing the GSO projection to any loop. (orig.)
Neutrality of the lorentz transformations in SRT
International Nuclear Information System (INIS)
Hamdan, N.; Baza, S.
2005-01-01
The special theory of Relativity (SRT), gives us two results, the dilation of time and the contraction of the Length, which have been refuted by many scientists. The solution to these kinematical effects has driven researchers to develop new methods. One of these methods is using the physical law equations and apply the principle of relativity to them. With this approach, we reformulated the SRT in a simple manner which has dynamical applications without using the Lorentz transformations (LT) and its kinematical effects. We obtained the results which require the invariant of Maxwell's field equations under the LT in a way different to that of Einsterin. In the present paper, we get the LT from the Lorentz force. In contrast to Einstein's LT with its kinematical effects, the LT produced in this paper is simply a neutral transformation. Containing no physical significance, i.e. LT and its kinematical effects do not explain any physical phenomenon. (author)
Sixth Meeting on CPT and Lorentz Symmetry
CPT and Lorentz Symmetry
2014-01-01
This book contains the Proceedings of the Sixth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on June 17–21, 2013. The Meeting focused on tests of these fundamental symmetries and on related theoretical issues, including scenarios for possible violations. Topics covered at the meeting include searches for CPT and Lorentz violations involving: accelerator and collider experiments; atomic, nuclear, and particle decays; birefringence, dispersion, and anisotropy in cosmological sources; clock-comparison measurements; electromagnetic resonant cavities and lasers; tests of the equivalence principle; gauge and Higgs particles; high-energy astrophysical observations; laboratory tests of gravity; matter interferometry; neutrino oscillations and propagation; oscillations and decays of neutral mesons; particle–antiparticle comparisons; post-newtonian gravity in the solar system and beyond; second- and third-generation particles; space-based missions; spectroscopy of hydrogen and ant...
Hiding Lorentz invariance violation with MOND
International Nuclear Information System (INIS)
Sanders, R. H.
2011-01-01
Horava-Lifshitz gravity is an attempt to construct a renormalizable theory of gravity by breaking the Lorentz invariance of the gravitational action at high energies. The underlying principle is that Lorentz invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low-energy limit of Horava-Lifshitz gravity in its nonprojectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than cH 0 ; this modification results in the phenomenology of modified Newtonian dynamics (MOND) at lower accelerations. As a relativistic theory of MOND, this modified Horava-Lifshitz theory presents several advantages over its predecessors.
Cobordism independence of Grassmann manifolds
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
ν(m) divides m. Given a positive integer d, let G(d) denote the set of bordism classes of all non-bounding. Grassmannian manifolds Gk(Fn+k) having real dimension d such that k < n. The restric- tion k
Lorentz violation and generalized uncertainty principle
Lambiase, Gaetano; Scardigli, Fabio
2018-04-01
Investigations on possible violation of Lorentz invariance have been widely pursued in the last decades, both from theoretical and experimental sides. A comprehensive framework to formulate the problem is the standard model extension (SME) proposed by A. Kostelecky, where violation of Lorentz invariance is encoded into specific coefficients. Here we present a procedure to link the deformation parameter β of the generalized uncertainty principle to the SME coefficients of the gravity sector. The idea is to compute the Hawking temperature of a black hole in two different ways. The first way involves the deformation parameter β , and therefore we get a deformed Hawking temperature containing the parameter β . The second way involves a deformed Schwarzschild metric containing the Lorentz violating terms s¯μ ν of the gravity sector of the SME. The comparison between the two different techniques yields a relation between β and s¯μ ν. In this way bounds on β transferred from s¯μ ν are improved by many orders of magnitude when compared with those derived in other gravitational frameworks. Also the opposite possibility of bounds transferred from β to s¯μ ν is briefly discussed.
Minimal genera of open 4-manifolds
Gompf, Robert E.
2013-01-01
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using the adjunction inequality for Stein surfaces. Smoothings can be constructed with much more control of these genus functions than the compact setting seems to allow. As an application, we expand the range of 4-manifolds known to have exotic smoothings (up to ...
Spectral gaps, inertial manifolds and kinematic dynamos
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)]. E-mail: mnjmhd@am.uva.es
2005-10-17
Inertial manifolds are desirable objects when ones wishes a dynamical process to behave asymptotically as a finite-dimensional ones. Recently [Physica D 194 (2004) 297] these manifolds are constructed for the kinematic dynamo problem with time-periodic velocity. It turns out, however, that the conditions imposed on the fluid velocity to guarantee the existence of inertial manifolds are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful because they represent different decay rates, but the classical dynamos where the magnetic field is maintained or grows are not covered by this approach, at least until more refined estimates are found.
Topology of high-dimensional manifolds
Energy Technology Data Exchange (ETDEWEB)
Farrell, F T [State University of New York, Binghamton (United States); Goettshe, L [Abdus Salam ICTP, Trieste (Italy); Lueck, W [Westfaelische Wilhelms-Universitaet Muenster, Muenster (Germany)
2002-08-15
The School on High-Dimensional Manifold Topology took place at the Abdus Salam ICTP, Trieste from 21 May 2001 to 8 June 2001. The focus of the school was on the classification of manifolds and related aspects of K-theory, geometry, and operator theory. The topics covered included: surgery theory, algebraic K- and L-theory, controlled topology, homology manifolds, exotic aspherical manifolds, homeomorphism and diffeomorphism groups, and scalar curvature. The school consisted of 2 weeks of lecture courses and one week of conference. Thwo-part lecture notes volume contains the notes of most of the lecture courses.
Analysis of mixed mode microwave distribution manifolds
International Nuclear Information System (INIS)
White, T.L.
1982-09-01
The 28-GHz microwave distribution manifold used in the ELMO Bumpy Torus-Scale (EBT-S) experiments consists of a toroidal metallic cavity, whose dimensions are much greater than a wavelength, fed by a source of microwave power. Equalization of the mixed mode power distribution ot the 24 cavities of EBT-S is accomplished by empirically adjusting the coupling irises which are equally spaced around the manifold. The performance of the manifold to date has been very good, yet no analytical models exist for optimizing manifold transmission efficiency or for scaling this technology to the EBT-P manifold design. The present report develops a general model for mixed mode microwave distribution manifolds based on isotropic plane wave sources of varying amplitudes that are distributed toroidally around the manifold. The calculated manifold transmission efficiency for the most recent EBT-S coupling iris modification is 90%. This agrees with the average measured transmission efficiency. Also, the model predicts the coupling iris areas required to balance the distribution of microwave power while maximizing transmission efficiency, and losses in waveguide feeds connecting the irises to the cavities of EBT are calculated using an approach similar to the calculation of mainfold losses. The model will be used to evaluate EBT-P manifold designs
Holomorphic bundles over elliptic manifolds
International Nuclear Information System (INIS)
Morgan, J.W.
2000-01-01
In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves
Method of construction of the Riemann function for a second-order hyperbolic equation
Aksenov, A. V.
2017-12-01
A linear hyperbolic equation of the second order in two independent variables is considered. The Riemann function of the adjoint equation is shown to be invariant with respect to the fundamental solutions transformation group. Symmetries and symmetries of fundamental solutions of the Euler-Poisson-Darboux equation are found. The Riemann function is constructed with the aid of fundamental solutions symmetries. Examples of the application of the algorithm for constructing Riemann function are given.
Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral
Directory of Open Access Journals (Sweden)
Weijing Zhao
2014-01-01
Full Text Available The derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses 2 derivative values at the endpoints. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.
On the $a$-points of the derivatives of the Riemann zeta function
Onozuka, Tomokazu
2016-01-01
We prove three results on the $a$-points of the derivatives of the Riemann zeta function. The first result is a formula of the Riemann-von Mangoldt type; we estimate the number of the $a$-points of the derivatives of the Riemann zeta function. The second result is on certain exponential sum involving $a$-points. The third result is an analogue of the zero density theorem. We count the $a$-points of the derivatives of the Riemann zeta function in $1/2-(\\log\\log T)^2/\\log T
Nonassociative geometry of manifold with trajectories
International Nuclear Information System (INIS)
Bouetou, T.B.; Matveev, O.A.
2004-12-01
We give some properties of solution of second order differential or system of differential equations on the manifold. It turns out that such manifolds can be seen as quasigroups or loop under certain circumstances. Output of the operations are given and the connection defined. (author)
Strictly convex functions on complete Finsler manifolds
Indian Academy of Sciences (India)
convex functions on the metric structures of complete Finsler manifolds. More precisely we discuss ... map expp at some point p ∈ M (and hence at every point on M) is defined on the whole tangent space Mp to M at ... The influence of the existence of convex functions on the metric and topology of under- lying manifolds has ...
Harmonic manifolds with minimal horospheres are flat
Indian Academy of Sciences (India)
Abstract. In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting ...
Harmonic Manifolds with Minimal Horospheres are Flat
Indian Academy of Sciences (India)
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem.
Hirzebruch genera of manifolds with torus action
International Nuclear Information System (INIS)
Panov, T E
2001-01-01
A quasitoric manifold is a smooth 2n-manifold M 2n with an action of the compact torus T n such that the action is locally isomorphic to the standard action of T n on C n and the orbit space is diffeomorphic, as a manifold with corners, to a simple polytope P n . The name refers to the fact that topological and combinatorial properties of quasitoric manifolds are similar to those of non-singular algebraic toric varieties (or toric manifolds). Unlike toric varieties, quasitoric manifolds may fail to be complex. However, they always admit a stably (or weakly almost) complex structure, and their cobordism classes generate the complex cobordism ring. Buchstaber and Ray have recently shown that the stably complex structure on a quasitoric manifold is determined in purely combinatorial terms, namely, by an orientation of the polytope and a function from the set of codimension-one faces of the polytope to primitive vectors of the integer lattice. We calculate the χ y -genus of a quasitoric manifold with a fixed stably complex structure in terms of the corresponding combinatorial data. In particular, this gives explicit formulae for the classical Todd genus and the signature. We also compare our results with well-known facts in the theory of toric varieties
Transversal lightlike submanifolds of indefinite sasakian manifolds
YILDIRIM, Cumali; Yıldırım, Cumali; Şahin, Bayram
2014-01-01
We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...
Transversal lightlike submanifolds of indefinite sasakian manifolds
YILDIRIM, Cumali
2010-01-01
We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical tr...
Holomorphic curves in exploded manifolds: Kuranishi structure
Parker, Brett
2013-01-01
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside a moduli stack of curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.
Rhodes, Tyler J.; Smolentsev, Sergey; Abdou, Mohamed
2018-05-01
Understanding magnetohydrodynamic (MHD) phenomena associated with the flow of electrically conducting fluids in complex geometry ducts subject to a strong magnetic field is required to effectively design liquid metal (LM) blankets for fusion reactors. Particularly, accurately predicting the 3D MHD pressure drop and flow distribution is important. To investigate these topics, we simulate a LM MHD flow through an electrically non-conducting prototypic manifold for a wide range of flow and geometry parameters using a 3D MHD solver, HyPerComp incompressible MHD solver for arbitrary geometry. The reference manifold geometry consists of a rectangular feeding duct which suddenly expands such that the duct thickness in the magnetic field direction abruptly increases by a factor rexp. Downstream of the sudden expansion, the LM is distributed into several parallel channels. As a first step in qualifying the flow, a magnitude of the curl of the induced Lorentz force was used to distinguish between inviscid, irrotational core flows and boundary and internal shear layers where inertia and/or viscous forces are important. Scaling laws have been obtained which characterize the 3D MHD pressure drop and flow balancing as a function of the flow parameters and the manifold geometry. Associated Hartmann and Reynolds numbers in the computations were ˜103 and ˜101-103, respectively, while rexp was varied from 4 to 12. An accurate model for the pressure drop was developed for the first time for inertial-electromagnetic and viscous-electromagnetic regimes based on 96 computed cases. Analysis shows that flow balance can be improved by lengthening the distance between the manifold inlet and the entrances of the parallel channels by utilizing the effect of flow transitioning to a quasi-two-dimensional state in the expansion region of the manifold.
Harmonic space and quaternionic manifolds
International Nuclear Information System (INIS)
Galperin, A.; Ogievetsky, O.; Ivanov, E.
1992-10-01
A principle of harmonic analyticity underlying the quaternionic (quaternion-Kaehler) geometry is found, and the differential constraints which define this geometry are solved. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group rotating the complex structures. An one-to-one correspondence is established between the quaternionic spaces and off-shell N=2 supersymmetric sigma-models coupled to N=2 supergravity. Coordinates of the analytic subspace are identified with superfields describing N=2 matter hypermultiplets and a compensating hypermultiplet of N=2 supergravity. As an illustration the potentials for the symmetric quaternionic spaces are presented. (K.A.) 22 refs
Moving Manifolds in Electromagnetic Fields
Directory of Open Access Journals (Sweden)
David V. Svintradze
2017-08-01
Full Text Available We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Function theory on symplectic manifolds
Polterovich, Leonid
2014-01-01
This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book provides an essentially self-contained introduction into these developments along with applications to symplectic topology, algebra and geometry of symplectomorphism groups, Hamiltonian dynamics and quantum mechanics. It will appeal to researchers and students from the graduate level onwards. I like the spirit of this book. It formulates concepts clearly and explains the relationship between them. The subject matter is i...
Conformal manifolds: ODEs from OPEs
Behan, Connor
2018-03-01
The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this question, we compute perturbative corrections to several observables in an abstract CFT, starting with the beta function. This yields a sum rule that the theory must obey in order to be part of a conformal manifold. The set of constraints relating CFT data at different values of the coupling can in principle be written as a dynamical system that allows one to flow arbitrarily far. We begin the analysis of it by finding a simple form for the differential equations when the spacetime and theory space are both one-dimensional. A useful feature we can immediately observe is that our system makes it very difficult for level crossing to occur.
Concerning the equivalence of Lorentz's and Einstein's theories
International Nuclear Information System (INIS)
Clube, S.V.M.
1978-01-01
A clear distinction is drawn between derivations of the Lorentz transformations by Lorentz and Einstein. The choice as to which derivation is correct is still open to experimental test. Possible reasons are given for preferring the Lorentz derivation in terms of a material aether, and the role of covariance in physical theory is considered to be heuristic rather than fundamental. The existence of a material aether also permits one to question the fundamental role of fields in modern theory
Are the invariance principles really truly Lorentz covariant?
International Nuclear Information System (INIS)
Arunasalam, V.
1994-02-01
It is shown that some sections of the invariance (or symmetry) principles such as the space reversal symmetry (or parity P) and time reversal symmetry T (of elementary particle and condensed matter physics, etc.) are not really truly Lorentz covariant. Indeed, I find that the Dirac-Wigner sense of Lorentz invariance is not in full compliance with the Einstein-Minkowski reguirements of the Lorentz covariance of all physical laws (i.e., the world space Mach principle)
Lorentz Violation, Möller Scattering, and Finite Temperature
Directory of Open Access Journals (Sweden)
Alesandro F. Santos
2018-01-01
Full Text Available Lorentz and CPT symmetries may be violated in new physics that emerges at very high energy scale, that is, at the Planck scale. The differential cross section of the Möller scattering due to Lorentz violation at finite temperature is calculated. Lorentz-violating effects emerge from an interaction vertex due to a CPT-odd nonminimal coupling in the covariant derivative. The finite temperature effects are determined using the Thermo Field Dynamics (TFD formalism.
Riemann-Cartan geometry of nonlinear disclination mechanics
Yavari, A.
2012-03-23
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).
Strongly not relatives Kähler manifolds
Directory of Open Access Journals (Sweden)
Zedda Michela
2017-02-01
Full Text Available In this paper we study Kähler manifolds that are strongly not relative to any projective Kähler manifold, i.e. those Kähler manifolds that do not share a Kähler submanifold with any projective Kähler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results which highlight some relations between this property and the existence of a full Kähler immersion into the infinite dimensional complex projective space. As application we get that the 1-parameter families of Bergman-Hartogs and Fock-Bargmann-Hartogs domains are strongly not relative to projective Kähler manifolds.
Heterotic model building: 16 special manifolds
International Nuclear Information System (INIS)
He, Yang-Hui; Lee, Seung-Joo; Lukas, Andre; Sun, Chuang
2014-01-01
We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list. The data for these models can be downloaded http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/toricdata/index.html.
A new General Lorentz Transformation model
International Nuclear Information System (INIS)
Novakovic, Branko; Novakovic, Alen; Novakovic, Dario
2000-01-01
A new general structure of Lorentz Transformations, in the form of General Lorentz Transformation model (GLT-model), has been derived. This structure includes both Lorentz-Einstein and Galilean Transformations as its particular (special) realizations. Since the free parameters of GLT-model have been identified in a gravitational field, GLT-model can be employed both in Special and General Relativity. Consequently, the possibilities of an unification of Einstein's Special and General Theories of Relativity, as well as an unification of electromagnetic and gravitational fields are opened. If GLT-model is correct then there exist four new observation phenomena (a length and time neutrality, and a length dilation and a time contraction). Besides, the well-known phenomena (a length contraction, and a time dilation) are also the constituents of GLT-model. It means that there is a symmetry in GLT-model, where the center of this symmetry is represented by a length and a time neutrality. A time and a length neutrality in a gravitational field can be realized if the velocity of a moving system is equal to the free fall velocity. A time and a length neutrality include an observation of a particle mass neutrality. A special consideration has been devoted to a correlation between GLT-model and a limitation on particle velocities in order to investigate the possibility of a travel time reduction. It is found out that an observation of a particle speed faster then c=299 792 458 m/s, is possible in a gravitational field, if certain conditions are fulfilled
Testing Lorentz invariance in β decay
Directory of Open Access Journals (Sweden)
Sytema A.
2014-03-01
Experimentally we exploit the Gamow-Teller transition of polarized 20Na, where we can test the dependence of the β-decay rate on the spin orientation of 20Na. The polarization degree is measured using the β asymmetry, while the decay rate is measured by the γ yield. A change in the γ rate, when reversing the spin, implies Lorentz invariance violation. The decay rate should depend on sidereal time and the polarization direction relative to the rotation axis of the earth. The method of the measurement will be presented, together with the first results.
Lorentz invariance with an invariant energy scale.
Magueijo, João; Smolin, Lee
2002-05-13
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
Mixed Lorentz boosted $Z^{0}'s$
Kjaer, N J
2001-01-01
A novel technique is proposed to study systematic errors on jet reconstruction in W physics measurements at LEP2 with high statistical precision. The method is based on the emulation of W pair events using Mixed Lorentz Boosted Z0 events. The scope and merits of the method and its statistical accuracy are discussed in the context of the DELPHI W mass measurement in the fully hadronic channel. The numbers presented are preliminary in the sense that they do not constitute the final DELPHI systematic errors.
Effective potential in Lorentz-breaking field theory models
Energy Technology Data Exchange (ETDEWEB)
Baeta Scarpelli, A.P. [Centro Federal de Educacao Tecnologica, Nova Gameleira Belo Horizonte, MG (Brazil); Setor Tecnico-Cientifico, Departamento de Policia Federal, Belo Horizonte, MG (Brazil); Brito, L.C.T. [Universidade Federal de Lavras, Departamento de Fisica, Lavras, MG (Brazil); Felipe, J.C.C. [Universidade Federal de Lavras, Departamento de Fisica, Lavras, MG (Brazil); Universidade Federal dos Vales do Jequitinhonha e Mucuri, Instituto de Engenharia, Ciencia e Tecnologia, Veredas, Janauba, MG (Brazil); Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil)
2017-12-15
We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and some examples of Lorentz-violating extensions of scalar QED. We observe, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we study depend on the background tensors responsible for the Lorentz-symmetry violation. This has consequences for physical quantities like, for example, in the induced mass due to the Coleman-Weinberg mechanism. (orig.)
Consistent Lorentz violation in flat and curved space
International Nuclear Information System (INIS)
Dvali, Gia; Pujolas, Oriol; Redi, Michele
2007-01-01
Motivated by the severity of the bounds on Lorentz violation in the presence of ordinary gravity, we study frameworks in which Lorentz violation does not affect the spacetime geometry. We show that there are at least two inequivalent classes of spontaneous Lorentz breaking that even in the presence of gravity result in Minkowski space. The first one generically corresponds to the condensation of tensor fields with tachyonic mass, which in turn is related to ghost condensation. In the second class, realized by the Dvali-Gabadadze-Porrati model or theories of massive gravitons, spontaneous Lorentz breaking is induced by the expectation value of sources. The generalization to de Sitter space is also discussed
Studies on representation of the Lorentz group and gauge theory
International Nuclear Information System (INIS)
Hanitriarivo, R.
2002-01-01
This work is focused on studies about the representation of the Lorentz group and gauge theory. The mathematical tools required for the different studies are presented, as well as for the representation of the Lorentz group and for the gauge theory. Representation of the Lorentz group gives the possible types of fields and wave functions that describe particles: fermions are described by spinors and bosons are described by scalar or vector. Each of these entities (spinors, scalars, vectors) are characterized by their behavior under the action of Lorentz transformations.Gauge theory is used to describe the interactions between particles. [fr
Effective potential in Lorentz-breaking field theory models
International Nuclear Information System (INIS)
Baeta Scarpelli, A.P.; Brito, L.C.T.; Felipe, J.C.C.; Nascimento, J.R.; Petrov, A.Yu.
2017-01-01
We calculate explicitly the one-loop effective potential in different Lorentz-breaking field theory models. First, we consider a Yukawa-like theory and some examples of Lorentz-violating extensions of scalar QED. We observe, for the extended QED models, that the resulting effective potential converges to the known result in the limit in which Lorentz symmetry is restored. Besides, the one-loop corrections to the effective potential in all the cases we study depend on the background tensors responsible for the Lorentz-symmetry violation. This has consequences for physical quantities like, for example, in the induced mass due to the Coleman-Weinberg mechanism. (orig.)
Integrable systems twistors, loop groups, and Riemann surfaces
Hitchin, NJ; Ward, RS
2013-01-01
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu
Bosonization in a two-dimensional Riemann Cartan geometry
International Nuclear Information System (INIS)
Denardo, G.; Spallucci, E.
1987-01-01
We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)
The Riemann zeta-function theory and applications
Ivic, Aleksandar
2003-01-01
""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim
Riemann-Roch Spaces and Linear Network Codes
DEFF Research Database (Denmark)
Hansen, Johan P.
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal...... number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\\cite{DBLP:journals/tit/KoetterK08} introduced...... in the above metric making them suitable for linear network coding....
Some impacts of Lorentz violation on cosmology
International Nuclear Information System (INIS)
Arianto; Zen, Freddy P.; Gunara, Bobby E.; Triyanta; Supardi
2007-01-01
The impact of Lorentz violation on the dynamics of a scalar field is investigated. In particular, we study the dynamics of a scalar field in the scalar-vector-tensor theory where the vector field is constrained to be unity and time like. By taking a generic form of the scalar field action, a generalized dynamical equation for the scalar-vector-tensor theory of gravity is obtained to describe the cosmological solutions. We present a class of exact solutions for an ordinary scalar field or phantom field corresponding to a power law coupling vector and the Hubble parameter. As the results, we find a constant equation of state in de Sitter space-time and power law expansion with the quadratic of coupling vector, while a dynamic equation of state is obtained for n > 2. Then, we consider the inflationary scenario based on the Lorentz violating scalar-vector-tensor theory of gravity with general power-law coupling vector and two typical potentials: inverse power-law and power-law potentials. In fact, both the coupling vector and the potential models affect the dynamics of the inflationary solutions. Finally, we use the dynamical system formalism to study the attractor behavior of a cosmological model containing a scalar field endowed with a quadratic coupling vector and a chaotic potential
Quantizations of D = 3 Lorentz symmetry
Energy Technology Data Exchange (ETDEWEB)
Lukierski, J. [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Tolstoy, V.N. [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow (Russian Federation)
2017-04-15
Using the isomorphism o(3; C) ≅ sl(2; C) we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r-matrices) for real forms o(3) and o(2,1) of the complex Lie algebra o(3; C) in terms of real forms of sl(2; C): su(2), su(1,1) and sl(2; R). We prove that the D = 3 Lorentz symmetry o(2,1) ≅ su(1,1) ≅ sl(2; R) has three different Hopf-algebraic quantum deformations, which are expressed in the simplest way by two standard su(1,1) and sl(2; R) q-analogs and by simple Jordanian sl(2; R) twist deformation. These quantizations are presented in terms of the quantum Cartan-Weyl generators for the quantized algebras su(1,1) and sl(2; R) as well as in terms of quantum Cartesian generators for the quantized algebra o(2,1). Finally, some applications of the deformed D = 3 Lorentz symmetry are mentioned. (orig.)
Cosmological constraints on Lorentz violating dark energy
Audren, B; Lesgourgues, J; Sibiryakov, S
2013-01-01
The role of Lorentz invariance as a fundamental symmetry of nature has been lately reconsidered in different approaches to quantum gravity. It is thus natural to study whether other puzzles of physics may be solved within these proposals. This may be the case for the cosmological constant problem. Indeed, it has been shown that breaking Lorentz invariance provides Lagrangians that can drive the current acceleration of the universe without experiencing large corrections from ultraviolet physics. In this work, we focus on the simplest model of this type, called ThetaCDM, and study its cosmological implications in detail. At the background level, this model cannot be distinguished from LambdaCDM. The differences appear at the level of perturbations. We show that in ThetaCDM, the spectrum of CMB anisotropies and matter fluctuations may be affected by a rescaling of the gravitational constant in the Poisson equation, by the presence of extra contributions to the anisotropic stress, and finally by the existence of ...
Cosmological constraints on Lorentz violating dark energy
Energy Technology Data Exchange (ETDEWEB)
Audren, B.; Lesgourgues, J. [FSB/ITP/LPPC, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland); Blas, D. [Theory Group, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Sibiryakov, S., E-mail: Benjamin.Audren@epfl.ch, E-mail: Diego.Blas@cern.ch, E-mail: Julien.Lesgourgues@cern.ch, E-mail: Sergey.Sibiryakov@cern.ch [Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow (Russian Federation)
2013-08-01
The role of Lorentz invariance as a fundamental symmetry of nature has been lately reconsidered in different approaches to quantum gravity. It is thus natural to study whether other puzzles of physics may be solved within these proposals. This may be the case for the cosmological constant problem. Indeed, it has been shown that breaking Lorentz invariance provides Lagrangians that can drive the current acceleration of the universe without experiencing large corrections from ultraviolet physics. In this work, we focus on the simplest model of this type, called ΘCDM, and study its cosmological implications in detail. At the background level, this model cannot be distinguished from ΛCDM. The differences appear at the level of perturbations. We show that in ΘCDM, the spectrum of CMB anisotropies and matter fluctuations may be affected by a rescaling of the gravitational constant in the Poisson equation, by the presence of extra contributions to the anisotropic stress, and finally by the existence of extra clustering degrees of freedom. To explore these modifications accurately, we modify the Boltzmann code class. We then use the parameter inference code Monte Python to confront ΘCDM with data from WMAP-7, SPT and WiggleZ. We obtain strong bounds on the parameters accounting for deviations from ΛCDM. In particular, we find that the discrepancy between the gravitational constants appearing in the Poisson and Friedmann equations is constrained at the level of 1.8%.
Extended KN algebras and extended conformal field theories over higher genus Riemann surfaces
International Nuclear Information System (INIS)
Ceresole, A.; Huang Chaoshang
1990-01-01
A global operator formalism for extended conformal field theories over higher genus Riemann surfaces is introduced and extended KN algebra are obtained by means of the KN bases. The BBSS construction of the spin-3 operator is carried out for Kac-Moody algebra A 2 over a Riemann surface of arbitrary genus. (orig.)
Superconformal structures and holomorphic 1/2-superdifferentials on N=1 super Riemann surfaces
International Nuclear Information System (INIS)
Kachkachi, H.; Kachkachi, M.
1992-07-01
Using the Super Riemann-Roch theorem we give a local expression for a holomorphic 1/2-superdifferential in a superconformal structure parametrized by special isothermal coordinates on an N=1 Super Riemann Surface (SRS). This construction is done by choosing a suitable origin for these coordinates. The holomorphy of the latter with respect to super Beltrami differentials is proven. (author). 26 refs
Superconformal algebra on meromorphic vector fields with three poles on super-Riemann sphere
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-07-01
Based upon the Riemann-Roch theorem, we construct superconformal algebra of meromorphic vector fields with three poles and the relevant abelian differential of the third kind on super Riemann sphere. The algebra includes two Ramond sectors as subalgebra, and implies a picture of interaction of three superstrings. (author). 14 refs
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin
2013-01-01
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Discriminative sparse coding on multi-manifolds
Wang, J.J.-Y.
2013-09-26
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.
Two-Loop Scattering Amplitudes from the Riemann Sphere
Geyer, Yvonne; Monteiro, Ricardo; Tourkine, Piotr
2016-01-01
The scattering equations give striking formulae for massless scattering amplitudes at tree level and, as shown recently, at one loop. The progress at loop level was based on ambitwistor string theory, which naturally yields the scattering equations. We proposed that, for ambitwistor strings, the standard loop expansion in terms of the genus of the worldsheet is equivalent to an expansion in terms of nodes of a Riemann sphere, with the nodes carrying the loop momenta. In this paper, we show how to obtain two-loop scattering equations with the correct factorization properties. We adapt genus-two integrands from the ambitwistor string to the nodal Riemann sphere and show that these yield correct answers, by matching standard results for the four-point two-loop amplitudes of maximal supergravity and super-Yang-Mills theory. In the Yang-Mills case, this requires the loop analogue of the Parke-Taylor factor carrying the colour dependence, which includes non-planar contributions.
Fractal supersymmetric QM, Geometric Probability and the Riemann Hypothesis
Castro, C
2004-01-01
The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form $ s_n =1/2+i\\lambda_n $. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. To test the validity of this geometric probabilistic framework to compute the probability if the RH is true, we apply it directly to the the hyperbolic sine function $ \\sinh (s) $ case which obeys a trivial analog of the RH (the HSRH). Its zeros are equally spaced in the imaginary axis $ s_n = 0 + i n \\pi $. The geometric probability to find a zero (and an infinity of zeros) in the imaginary axis is exactly unity. We proceed with a fractal supersymme...
Large chiral diffeomorphisms on Riemann surfaces and W-algebras
International Nuclear Information System (INIS)
Bandelloni, G.; Lazzarini, S.
2006-01-01
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims
International Nuclear Information System (INIS)
Chiang, Yuan-Jen.
1989-01-01
Harmonic maps between manifolds are described as the critical maps of their associated energy functionals. By using Sampson's method [Sam1], the author constructs a Sobolev's chain on a compact V-manifold and obtain Rellich's Theorem (Theorem 3.1), Sobolev's Theorem (Theorem 3.2), the regularity theorem (Theorem 3.3), the property of the eigenspaces for the Laplacian (Theorem 3.5) and the solvability of Laplacian (Theorem 3.6). Then, with these results, he constructs the Green's functions for the Laplacian on a compact V-manifold M in Proposition 4.1; and obtain an orthonormal basis for L 2 (M) formed by the eigenfunctions of the Laplacian corresponding to the eigenvalues in Proposition 4.2. He also estimates the eigenvalues and eigenfunctions of the Laplacian in Theorem 4.3, which is used to construct the heat kernel on a compact V-manifold in Proposition 5.1. Afterwards, he compares the G-invariant heat kernel functions with the G-invariant fundamental solutions of heat equations in the finite V-charts of a compact V-manifold in Theorem 6.1, and then study two integral operators associated to the heat kernel on a compact V-manifold in section 7. With all the preceding results established, in Theorem 8.3 he uses successive approximations to prove the existence of the solutions of parabolic equations on V-manifolds. Finally, he uses Theorem 8.3 to show the existence of harmonic maps from compact V-manifolds into compact Riemannian manifolds in Theorem 9.1 which extends Eells-Sampson's results [E-S
Space time manifolds and contact structures
Directory of Open Access Journals (Sweden)
K. L. Duggal
1990-01-01
Full Text Available A new class of contact manifolds (carring a global non-vanishing timelike vector field is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.
Introduction to Ives' 'Derivation of the Lorentz transformations'
International Nuclear Information System (INIS)
Ruderfer, M.
1979-01-01
Lorentz ether theory is elevated on a par with special relativity by Ives' derivation of the Lorentz transformations. The two theories combined then demand the physical existence of a relativistic ether. This is supported by the still unfolding hierarchy of matter. Cogent implications for physical theory follow. (Auth.)
Vortex deformation and reduction of the Lorentz force
International Nuclear Information System (INIS)
Vuorio, M.
1977-01-01
A vortex of an extreme II-type superconductor is considered in the presence of a transport current. The equivalence of Magnus and Lorentz forces in a static vortex is discussed and the effect of vortex deformation is included in calculating corrections to the conventional expression of the Lorentz force. (author)
Lorentz Invariant Spectrum of Minimal Chiral Schwinger Model
Kim, Yong-Wan; Kim, Seung-Kook; Kim, Won-Tae; Park, Young-Jai; Kim, Kee Yong; Kim, Yongduk
We study the Lorentz transformation of the minimal chiral Schwinger model in terms of the alternative action. We automatically obtain a chiral constraint, which is equivalent to the frame constraint introduced by McCabe, in order to solve the frame problem in phase space. As a result we obtain the Lorentz invariant spectrum in any moving frame by choosing a frame parameter.
Path integrals on curved manifolds
International Nuclear Information System (INIS)
Grosche, C.; Steiner, F.
1987-01-01
A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correction ΔV ∝ ℎ 2 from the classical Lagrangian L, i.e. the correct effective Lagrangian to be used in the path integral is L eff = L-ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: The d-dimensional rotator, i.e. the motion on the sphere S d-1 , the path integral in d-dimensional polar coordinates, the exact treatment of the hydrogen atom in R 2 and R 3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential. (orig.)
One-dimensional super Calabi-Yau manifolds and their mirrors
Energy Technology Data Exchange (ETDEWEB)
Noja, S. [Dipartimento di Matematica, Università degli Studi di Milano,Via Saldini 50, I-20133 Milano (Italy); Cacciatori, S.L. [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); INFN, Sezione di Milano,Via Celoria 16, I-20133 Milano (Italy); Piazza, F. Dalla [Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio 11, I-22100 Como (Italy); Marrani, A. [Centro Studi e Ricerche ‘Enrico Fermi’,Via Panisperna 89A, I-00184 Roma (Italy); Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova,and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padova (Italy); Re, R. [Dipartimento di Matematica e Informatica, Università degli Studi di Catania,Viale Andrea Doria 6, 95125 Catania (Italy)
2017-04-18
We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY’s having reduced manifold equal to ℙ{sup 1}, namely the projective super space ℙ{sup 1|2} and the weighted projective super space Wℙ{sub (2)}{sup 1|1}. Then we compute the corresponding sheaf cohomology of superforms, showing that the cohomology with picture number one is infinite dimensional, while the de Rham cohomology, which is what matters from a physical point of view, remains finite dimensional. Moreover, we provide the complete real and holomorphic de Rham cohomology for generic projective super spaces ℙ{sup n|m}. We also determine the automorphism groups: these always match the dimension of the projective super group with the only exception of ℙ{sup 1|2}, whose automorphism group turns out to be larger than the projective super group. By considering the cohomology of the super tangent sheaf, we compute the deformations of ℙ{sup 1|m}, discovering that the presence of a fermionic structure allows for deformations even if the reduced manifold is rigid. Finally, we show that ℙ{sup 1|2} is self-mirror, whereas Wℙ{sub (2)}{sup 1|1} has a zero dimensional mirror. Also, the mirror map for ℙ{sup 1|2} naturally endows it with a structure of N=2 super Riemann surface.
Lorentz violation, gravitoelectromagnetism and Bhabha scattering at finite temperature
Santos, A. F.; Khanna, Faqir C.
2018-04-01
Gravitoelectromagnetism (GEM) is an approach for the gravitation field that is described using the formulation and terminology similar to that of electromagnetism. The Lorentz violation is considered in the formulation of GEM that is covariant in its form. In practice, such a small violation of the Lorentz symmetry may be expected in a unified theory at very high energy. In this paper, a non-minimal coupling term, which exhibits Lorentz violation, is added as a new term in the covariant form. The differential cross-section for Bhabha scattering in the GEM framework at finite temperature is calculated that includes Lorentz violation. The Thermo Field Dynamics (TFD) formalism is used to calculate the total differential cross-section at finite temperature. The contribution due to Lorentz violation is isolated from the total cross-section. It is found to be small in magnitude.
Modelling Planck-scale Lorentz violation via analogue models
International Nuclear Information System (INIS)
Weinfurtner, Silke; Liberati, Stefano; Visser, Matt
2006-01-01
Astrophysical tests of Planck-suppressed Lorentz violations had been extensively studied in recent years and very stringent constraints have been obtained within the framework of effective field theory. There are however still some unresolved theoretical issues, in particular regarding the so called 'naturalness problem' - which arises when postulating that Planck suppressed Lorentz violations arise only from operators with mass dimension greater than four in the Lagrangian. In the work presented here we shall try to address this problem by looking at a condensed-matter analogue of the Lorentz violations considered in quantum gravity phenomenology. specifically, we investigate the class of two-component BECs subject to laserinduced transitions between the two components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. We shall show that such a model can be considered to be an explicit example high-energy Lorentz violations where the 'naturalness problem' does not arise
Pseudo-Kaehler quantization on flag manifolds
International Nuclear Information System (INIS)
Karabegov, A.V.
1997-07-01
A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. In particular cases we arrive at Berezin's quantization via covariant and contravariant symbols. (author). 16 refs
The Hodge theory of projective manifolds
de Cataldo, Mark Andrea
2007-01-01
This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds. It assumes very little background and aims at describing how the theory becomes progressively richer and more beautiful as one specializes from Riemannian, to Kähler, to complex projective manifolds. Though the proof of the Hodge Theorem is omitted, its consequences - topological, geometrical and algebraic - are discussed at some length. The special properties of complex projective manifolds constitute an important body of knowledge and readers are guided through it with the help of selected exercises. Despite starting with very few prerequisites, the concluding chapter works out, in the meaningful special case of surfaces, the proof of a special property of maps between complex projective manifolds, which was discovered only quite recently.
Project Development Specification for Valve Pit Manifold
International Nuclear Information System (INIS)
MCGREW, D.L.
2000-01-01
Establishes the performance, design development, and test requirements for the valve pit manifolds. The system engineering approach was used to develop this document in accordance with the guidelines laid out in the Systems Engineering Management Plan for Project W-314
Moduli space of Calabi-Yau manifolds
International Nuclear Information System (INIS)
Candelas, P.; De la Ossa, X.C.
1991-01-01
We present an accessible account of the local geometry of the parameter space of Calabi-Yau manifolds. It is shown that the parameter space decomposes, at least locally, into a product with the space of parameters of the complex structure as one factor and a complex extension of the parameter space of the Kaehler class as the other. It is also shown that each of these spaces is itself a Kaehler manifold and is moreover a Kaehler manifold of restricted type. There is a remarkable symmetry in the intrinsic structures of the two parameter spaces and the relevance of this to the conjectured existence of mirror manifolds is discussed. The two parameter spaces behave differently with respect to modular transformations and it is argued that the role of quantum corrections is to restore the symmetry between the two types of parameters so as to enforce modular invariance. (orig.)
Indian Academy of Sciences (India)
Kähler–Norden manifolds using the theory of Tachibana operators is presented. ... arguments is subject to the action of the affinor structure ϕ. ..... [20] Vishnevskii V V, Integrable affinor structures and their plural interpretations, J. Math. Sci.
Submanifolds of a Finsler manifold - I
International Nuclear Information System (INIS)
Rastogi, S.C.
1986-06-01
In 1981, Hojo defined a scalar function φ (p) (x,y), where p is a real number (not= 1). He used this function to define a tensor φ ij (p) (x,y) and a c P Γ-connection which reduce to g ij (x,y) and cΓ-connection for p=2. The aim of this paper is to study submanifolds of a Finsler manifold admitting a c P Γ-connection. In this paper I have obtained four kinds of Gauss-Codazzi equations based on various derivatives in a Finsler manifold admitting a c P Γ-connection. The method used in this paper is similar to the one used by the author in obtaining generalized Gauss-Codazzi equations based on congruences of curves in a Finsler manifold. Besides considering some special cases we have also studied the relationship between the Riemannian curvatures and Ricci tensors of the submanifold and the enveloping manifold. (author)
Generalized regular genus for manifolds with boundary
Directory of Open Access Journals (Sweden)
Paola Cristofori
2003-05-01
Full Text Available We introduce a generalization of the regular genus, a combinatorial invariant of PL manifolds ([10], which is proved to be strictly related, in dimension three, to generalized Heegaard splittings defined in [12].
Polynomial chaos representation of databases on manifolds
Energy Technology Data Exchange (ETDEWEB)
Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)
2017-04-15
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Geometry of superconformal manifolds. Part 1
International Nuclear Information System (INIS)
Roslyi, A.A.; Schwarz, A.S.; Voronov, A.A.
1987-01-01
The main facts about complex curves are generalized to superconformal manifolds. The results thus obtained are relevant to the dermion string theory and, in particular, they are useful for computation of determinants of superlaplacians which enter the string partition function
Stable harmonic maps from complete manifolds
International Nuclear Information System (INIS)
Xin, Y.L.
1986-01-01
By choosing distinguished cross-sections in the second variational formula for harmonic maps from manifolds with not too fast volume growth into certain submanifolds in the Euclidean space some Liouville type theorems have been proved in this article. (author)
Bumpy black holes from spontaneous Lorentz violation
International Nuclear Information System (INIS)
Dubovsky, Sergei; Tinyakov, Peter; Zaldarriaga, Matias
2007-01-01
We consider black holes in Lorentz violating theories of massive gravity. We argue that in these theories black hole solutions are no longer universal and exhibit a large number of hairs. If they exist, these hairs probe the singularity inside the black hole providing a window into quantum gravity. The existence of these hairs can be tested by future gravitational wave observatories. We generically expect that the effects we discuss will be larger for the more massive black holes. In the simplest models the strength of the hairs is controlled by the same parameter that sets the mass of the graviton (tensor modes). Then the upper limit on this mass coming from the inferred gravitational radiation emitted by binary pulsars implies that hairs are likely to be suppressed for almost the entire mass range of the super-massive black holes in the centers of galaxies
Inverse Scattering, the Coupling Constant Spectrum, and the Riemann Hypothesis
International Nuclear Information System (INIS)
Khuri, N. N.
2002-01-01
It is well known that the s-wave Jost function for a potential, λV, is an entire function of λ with an infinite number of zeros extending to infinity. For a repulsive V, and at zero energy, these zeros of the 'coupling constant', λ, will all be real and negative, λ n (0) n n =1/2+iγ n . Thus, finding a repulsive V whose coupling constant spectrum coincides with the Riemann zeros will establish the Riemann hypothesis, but this will be a very difficult and unguided search.In this paper we make a significant enlargement of the class of potentials needed for a generalization of the above idea. We also make this new class amenable to construction via inverse scattering methods. We show that all one needs is a one parameter class of potentials, U(s;x), which are analytic in the strip, 0≤Res≤1, Ims>T 0 , and in addition have an asymptotic expansion in powers of [s(s-1)] -1 , i.e. U(s;x)=V 0 (x)+gV 1 (x)+g 2 V 2 (x)+...+O(g N ), with g=[s(s-1)] -1 . The potentials V n (x) are real and summable. Under suitable conditions on the V n 's and the O(g N ) term we show that the condition, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx≠0, where f 0 is the zero energy and g=0 Jost function for U, is sufficient to guarantee that the zeros g n are real and, hence, s n =1/2+iγ n , for γ n ≥T 0 .Starting with a judiciously chosen Jost function, M(s,k), which is constructed such that M(s,0) is Riemann's ξ(s) function, we have used inverse scattering methods to actually construct a U(s;x) with the above properties. By necessity, we had to generalize inverse methods to deal with complex potentials and a nonunitary S-matrix. This we have done at least for the special cases under consideration.For our specific example, ∫ 0 ∞ vertical bar f 0 (x) vertical bar 2 V 1 (x) dx=0 and, hence, we get no restriction on Img n or Res n . The reasons for the vanishing of the above integral are given, and they give us hints on what one needs to proceed further. The problem
Noncommutative gauge theory for Poisson manifolds
Energy Technology Data Exchange (ETDEWEB)
Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de
2000-09-25
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Noncommutative gauge theory for Poisson manifolds
International Nuclear Information System (INIS)
Jurco, Branislav; Schupp, Peter; Wess, Julius
2000-01-01
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem
Sasakian manifolds and M-theory
International Nuclear Information System (INIS)
Figueroa-O’Farrill, José; Santi, Andrea
2016-01-01
We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of η-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterizing them in terms of generalized Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a new class of such backgrounds, extending previous work of Haupt, Lukas and Stelle. (paper)
Computer calculation of Witten's 3-manifold invariant
International Nuclear Information System (INIS)
Freed, D.S.; Gompf, R.E.
1991-01-01
Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant. (orig.)
Singular reduction of Nambu-Poisson manifolds
Das, Apurba
The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.
Online Manifold Regularization by Dual Ascending Procedure
Sun, Boliang; Li, Guohui; Jia, Li; Zhang, Hui
2013-01-01
We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approache...
Lorentz Violation in Warped Extra Dimensions
International Nuclear Information System (INIS)
Rizzo, Thomas G.
2011-01-01
Higher dimensional theories which address some of the problematic issues of the Standard Model(SM) naturally involve some form of D = 4 + n-dimensional Lorentz invariance violation (LIV). In such models the fundamental physics which leads to, e.g., field localization, orbifolding, the existence of brane terms and the compactification process all can introduce LIV in the higher dimensional theory while still preserving 4-d Lorentz invariance. In this paper, attempting to capture some of this physics, we extend our previous analysis of LIV in 5-d UED-type models to those with 5- d warped extra dimensions. To be specific, we employ the 5-d analog of the SM Extension of Kostelecky et al. which incorporates a complete set of operators arising from spontaneous LIV. We show that while the response of the bulk scalar, fermion and gauge fields to the addition of LIV operators in warped models is qualitatively similar to what happens in the flat 5-d UED case, the gravity sector of these models reacts very differently than in flat space. Specifically, we show that LIV in this warped case leads to a non-zero bulk mass for the 5-d graviton and so the would-be zero mode, which we identify as the usual 4-d graviton, must necessarily become massive. The origin of this mass term is the simultaneous existence of the constant non-zero AdS 5 curvature and the loss of general co-ordinate invariance via LIV in the 5-d theory. Thus warped 5-d models with LIV in the gravity sector are not phenomenologically viable.
The manifold model for space-time
International Nuclear Information System (INIS)
Heller, M.
1981-01-01
Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)
Right-angled polyhedra and hyperbolic 3-manifolds
Vesnin, A. Yu.
2017-04-01
Hyperbolic 3-manifolds whose fundamental groups are subgroups of finite index in right-angled Coxeter groups are under consideration. The construction of such manifolds is associated with regular colourings of the faces of polyhedra and, in particular, with 4-colourings. The following questions are discussed: the structure of the set of right-angled polytopes in Lobachevskii space; examples of orientable and non-orientable manifolds, including the classical Löbell manifold constructed in 1931; connections between the Hamiltonian property of a polyhedron and the existence of hyperelliptic involutions of manifolds; the volumes and complexity of manifolds; isometry between hyperbolic manifolds constructed from 4-colourings. Bibliography: 89 titles.
On some classes of super quasi-Einstein manifolds
International Nuclear Information System (INIS)
Ozguer, Cihan
2009-01-01
Quasi-Einstein and generalized quasi-Einstein manifolds are the generalizations of Einstein manifolds. In this study, we consider a super quasi-Einstein manifold, which is another generalization of an Einstein manifold. We find the curvature characterizations of a Ricci-pseudosymmetric and a quasi-conformally flat super quasi-Einstein manifolds. We also consider the condition C ∼ .S=0 on a super quasi-Einstein manifold, where C ∼ and S denote the quasi-conformal curvature tensor and Ricci tensor of the manifold, respectively.
Polynomials, Riemann surfaces, and reconstructing missing-energy events
Gripaios, Ben; Webber, Bryan
2011-01-01
We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.
Supersymmetric Dirac particles in Riemann-Cartan space-time
International Nuclear Information System (INIS)
Rumpf, H.
1981-01-01
A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of h/2π and thus complete the partial results of previous WKB calculations. The author also considers such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass. (Auth.)
A New Riemann Type Hydrodynamical Hierarchy and its Integrability Analysis
International Nuclear Information System (INIS)
Golenia, Jolanta Jolanta; Bogolubov, Nikolai N. Jr.; Popowicz, Ziemowit; Pavlov, Maxim V.; Prykarpatsky, Anatoliy K.
2009-12-01
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible co-symplectic structures and Lax type representations for the special cases N = 2, 3 and N = 4 are constructed. (author)
On Riemannian manifolds (Mn, g) of quasi-constant curvature
International Nuclear Information System (INIS)
Rahman, M.S.
1995-07-01
A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs
The Picard group of the moduli space of r-Spin Riemann surfaces
DEFF Research Database (Denmark)
Randal-Williams, Oscar
2012-01-01
An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford...... conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles....
Directory of Open Access Journals (Sweden)
Xuefeng Wei
2016-12-01
Full Text Available This article concerns the wave interaction problem for a strictly hyperbolic system of conservation laws whose Riemann solutions involve delta shock waves. To cover all situations, the global solutions are constructed when the initial data are taken as three piecewise constant states. It is shown that the Riemann solutions are stable with respect to a specific small perturbation of the Riemann initial data. In addition, some interesting nonlinear phenomena are captured during the process of constructing the solutions, such as the generation and decomposition of delta shock waves.
New complete noncompact Spin(7) manifolds
International Nuclear Information System (INIS)
Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.
2002-01-01
We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8
Factoring the dispersion relation in the presence of Lorentz violation
International Nuclear Information System (INIS)
Colladay, Don; McDonald, Patrick; Mullins, David
2010-01-01
We produce an explicit formula for the dispersion relation for the Dirac equation in the standard model extension in the presence of Lorentz violation. Our expression is obtained using novel techniques which exploit the algebra of quaternions. The dispersion relation is found to conveniently factor in two special cases that each involve a mutually exclusive set of nonvanishing Lorentz-violating parameters. This suggests that a useful approach to studies of Lorentz-violating models is to split the parameter space into two separate pieces, each of which yields a simple, tractable dispersion relation that can be used for analysis.
Rotation associated with product of two Lorentz transformations
International Nuclear Information System (INIS)
Van Wyk, C.B.
1984-01-01
In the usual presentation of the Lorentz transformation there is an almost complete absence of the use of products of these transformations. One of the reasons for this appears to be the large amount of calculation involved when multi-plying the 4X4 matrices of the vector representation of the Lorentz transformation. In the article this problem is partly cleared up by using the coordinate free two-component spinor representation of rotations and Lorentz transformations. It is also shown that the theory derived in the article can be applied to Thomas precission in a very simple and direct way
Strong binary pulsar constraints on Lorentz violation in gravity.
Yagi, Kent; Blas, Diego; Yunes, Nicolás; Barausse, Enrico
2014-04-25
Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of general relativity. One of these is Lorentz symmetry, which states that physical phenomena appear the same for all inertially moving observers. We study the effect of violations of Lorentz symmetry in the orbital evolution of binary pulsars and find that it induces a much more rapid decay of the binary's orbital period due to the emission of dipolar radiation. The absence of such behavior in recent observations allows us to place the most stringent constraints on Lorentz violation in gravity, thus verifying one of the cornerstones of Einstein's theory much more accurately than any previous gravitational observation.
Generalizations of teleparallel gravity and local Lorentz symmetry
International Nuclear Information System (INIS)
Sotiriou, Thomas P.; Barrow, John D.; Li Baojiu
2011-01-01
We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism.
Strong Binary Pulsar Constraints on Lorentz Violation in Gravity
Yagi, Kent; Yunes, Nicolas; Barausse, Enrico
2014-01-01
Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of General Relativity. One of these is Lorentz symmetry which states that physical phenomena appear the same for all inertially moving observers. We study the effect of violations of Lorentz symmetry in the orbital evolution of binary pulsars and find that it induces a much more rapid decay of the binary's orbital period due to the emission of dipolar radiation. The absence of such behavior in recent observations allows us to place the most stringent constraints on Lorentz violation in gravity, thus verifying one of the cornerstones of Einstein's theory much more accurately than any previous gravitational observation.
QED on curved background and on manifolds with boundaries: Unitarity versus covariance
International Nuclear Information System (INIS)
Vassilevich, D.V.
1994-11-01
Some recent results show that the covariant path integral and the integral over physical degrees of freedom give contradicting results on curved background and on manifolds with boundaries. This looks like a conflict between unitarity and covariance. We argue that this effect is due to the use of non-covariant measure on the space of physical degrees of freedom. Starting with the reduced phase space path integral and using covariant measure throughout computations we recover standard path integral in the Lorentz gauge and the Moss and Poletti BRST-invariant boundary conditions. We also demonstrate by direct calculations that in the approach based on Gaussian path integral on the space of physical degrees of freedom some basic symmetries are broken. (author). 39 refs
Uniformly bounded representations of the Lorentz groups
International Nuclear Information System (INIS)
Brega, A.O.
1982-01-01
For the Lorentz group G = SO/sub e/(n + 1, 1)(ngreater than or equal to 2) the author constructs a family of uniformly bounded representations by means of analytically continuing a certain normalization of the unitary principal series. The method the author uses relies on an analysis of various operators under a Mellin transform and extends earlier work of E.N. Wilson. In a series of papers Kunze and Stein initiated the theory of uniformly bounded representations of semisimple Lie groups; the starting point is the unitary principal series T(sigma,s) obtained in a certain subgroup M of G and a purely imaginary number s. From there Kunze and Stein constructed families of representations R(sigma,s) depending analytically on a parameter s in a domain D of C containing the imaginary axis which are unitarily equilvalent to T(sigma,s) for s contained in the set of imaginary numbers and whose operator norms are uniformly bounded for each s in D. In the case of the Lorentz groups SO/sub e/(n + 1, 1)(ngreater than or equal to2) and the trivial representation 1 of M, E.N. Wilson obtained such a family R(1,s) for the domain D = [s contained in the set of C: absolute value Re(s) Vertical Bar2]. For this domain D and for any representation sigma of M the author provides a family R(sigma,s) of uniformly bounded representations analytically continuing T(sigma,s), thereby generalizing Wilson's work. The author has also investigated certain symmetry properties of the representations R(sigma,s) under the action of the Weyl group. The trivial representation is Weyl group invariant and the family R(1,s) obtained by Wilson satisfies R(1,s) = R(1,-s) reflecting this. Obtained was the analogous result R(sigma,s) = R(sigma,-s) for some well known representations sigma that are Weyl group invariant. This involves the explicit computation of certain constants arising in the Fourier transforms of intertwining operators
Unsupervised image matching based on manifold alignment.
Pei, Yuru; Huang, Fengchun; Shi, Fuhao; Zha, Hongbin
2012-08-01
This paper challenges the issue of automatic matching between two image sets with similar intrinsic structures and different appearances, especially when there is no prior correspondence. An unsupervised manifold alignment framework is proposed to establish correspondence between data sets by a mapping function in the mutual embedding space. We introduce a local similarity metric based on parameterized distance curves to represent the connection of one point with the rest of the manifold. A small set of valid feature pairs can be found without manual interactions by matching the distance curve of one manifold with the curve cluster of the other manifold. To avoid potential confusions in image matching, we propose an extended affine transformation to solve the nonrigid alignment in the embedding space. The comparatively tight alignments and the structure preservation can be obtained simultaneously. The point pairs with the minimum distance after alignment are viewed as the matchings. We apply manifold alignment to image set matching problems. The correspondence between image sets of different poses, illuminations, and identities can be established effectively by our approach.
Lorentz invariance violation in modified gravity
International Nuclear Information System (INIS)
Brax, Philippe
2012-01-01
We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.
ICECUBE NEUTRINOS AND LORENTZ INVARIANCE VIOLATION
Energy Technology Data Exchange (ETDEWEB)
Amelino-Camelia, Giovanni [Dipartimento di Fisica, Sapienza Università di Roma and INFN, Sez. Roma1, P.le A. Moro 2, I-00185 Roma (Italy); Guetta, D. [Osservatorio astronomico di Roma, v. Frascati 33, I-00040 Monte Porzio Catone (Italy); Piran, Tsvi [The Racah Institute for Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2015-06-20
The IceCube neutrino telescope has found so far no evidence of gamma-ray burst (GRB) neutrinos. We here notice that these results assume the same travel times from source to telescope for neutrinos and photons, an assumption that is challenged by some much-studied pictures of spacetime quantization. We briefly review previous results suggesting that limits on quantum-spacetime effects obtained for photons might not be applicable to neutrinos, and we then observe that the outcome of GRB-neutrino searches could depend strongly on whether one allows for neutrinos to be affected by the minute effects of Lorentz invariance violation (LIV) predicted by some relevant quantum-spacetime models. We discuss some relevant issues using as an illustrative example three neutrinos that were detected by IceCube in good spatial coincidence with GRBs, but hours before the corresponding gamma rays. In general, this could happen if the earlier arrival reflects quantum-spacetime-induced LIV, but, as we stress, some consistency criteria must be enforced in order to properly test such a hypothesis. Our analysis sets the stage for future GRB-neutrino searches that could systematically test the possibility of quantum-spacetime-induced LIV.
Lorentz invariance violation in modified gravity
Energy Technology Data Exchange (ETDEWEB)
Brax, Philippe, E-mail: philippe.brax@cea.fr [Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France)
2012-06-06
We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.
Direct Lorentz force compensation flowmeter for electrolytes
Energy Technology Data Exchange (ETDEWEB)
Vasilyan, S., E-mail: suren.vasilyan@tu-ilmenau.de; Froehlich, Th. [Institute of Process Measurement and Sensor Technology, Ilmenau University of Technology, 98684 Ilmenau (Germany)
2014-12-01
A simplified method of contactless Lorentz force (LF) measurements for flow meters on electrolytes is described and realized. Modification and comparative representation are discussed against recently well-developed methods. Based on the catapult effect, that current carrying conductor experiences a repulsive force in a magnetic field, we demonstrate force measurement method of LF velocimetry applications by commonly known “electromagnetic force” compensation principle. Measurement approach through zero point stability is considered to minimize mechanical influences and avoid gravimetric uncertainties. Here, the current carrying wires are static fixed in the vicinity of magnet system at zero point stable position, while occurring deflection of magnets by electrolyte flow is compensated by external applied current within wires. Measurements performed by developed servo-system which drives control loop by means of optical position sensor for simplified (i) single wire and (ii) coil-like extended compensation schemes. Guided by experiments on electrolyte flow, we demonstrate the applicability of adopted principle for conductivities ranging from 2 to 20 S/m. Further improvements are discussed in agreement with the parameters of demonstration setup, straightforward theory, and experimental results. We argue that this method is potentially suitable for: (a) applications with higher conductivity like molten metal (order of 10{sup 6 }S/m) assuming spatial configuration of setup and (b) for lower range of conductivity (below 1 S/m) while this is strongly subject to stiffness of system and noise mainly mechanical and thermal radiations.
Traveling solitons in Lorentz and CPT breaking systems
International Nuclear Information System (INIS)
Souza Dutra, A. de; Correa, R. A. C.
2011-01-01
In this work we present a class of traveling solitons in Lorentz and CPT breaking systems. In the case of Lorentz violating scenarios, as far as we know, only static solitonic configurations were analyzed up to now in the literature. Here it is shown that it is possible to construct some traveling solitons which cannot be mapped into static configurations by means of Lorentz boosts due to explicit breaking. In fact, the traveling solutions cannot be reached from the static ones by using something similar to a Lorentz boost in those cases. Furthermore, in the model studied, a complete set of exact solutions is obtained. The solutions present a critical behavior controlled by the choice of an arbitrary integration constant.
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Directory of Open Access Journals (Sweden)
Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
National Research Council Canada - National Science Library
Derbyshire, John
2003-01-01
.... Is the hypothesis true or false?Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence...
Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition
Directory of Open Access Journals (Sweden)
Ge-Feng Yang
2012-01-01
differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.
Slow Invariant Manifolds in Chemically Reactive Systems
Paolucci, Samuel; Powers, Joseph M.
2006-11-01
The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.
Online Manifold Regularization by Dual Ascending Procedure
Directory of Open Access Journals (Sweden)
Boliang Sun
2013-01-01
Full Text Available We propose a novel online manifold regularization framework based on the notion of duality in constrained optimization. The Fenchel conjugate of hinge functions is a key to transfer manifold regularization from offline to online in this paper. Our algorithms are derived by gradient ascent in the dual function. For practical purpose, we propose two buffering strategies and two sparse approximations to reduce the computational complexity. Detailed experiments verify the utility of our approaches. An important conclusion is that our online MR algorithms can handle the settings where the target hypothesis is not fixed but drifts with the sequence of examples. We also recap and draw connections to earlier works. This paper paves a way to the design and analysis of online manifold regularization algorithms.
Dynamics and control of Lorentz-augmented spacecraft relative motion
Yan, Ye; Yang, Yueneng
2017-01-01
This book develops a dynamical model of the orbital motion of Lorentz spacecraft in both unperturbed and J2-perturbed environments. It explicitly discusses three kinds of typical space missions involving relative orbital control: spacecraft hovering, rendezvous, and formation flying. Subsequently, it puts forward designs for both open-loop and closed-loop control schemes propelled or augmented by the geomagnetic Lorentz force. These control schemes are entirely novel and represent a significantly departure from previous approaches.
Lorentz and CPT violation in QED revisited: A missing analysis
Energy Technology Data Exchange (ETDEWEB)
Del Cima, Oswaldo M., E-mail: wadodelcima@if.uff.b [Universidade Federal Fluminense (UFF), Polo Universitario de Rio das Ostras, Rua Recife s/n, 28890-000, Rio das Ostras, RJ (Brazil); Fonseca, Jakson M., E-mail: jakson.fonseca@ufv.b [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Avenida Peter Henry Rolfs s/n, 36570-000, Vicosa, MG (Brazil); Franco, Daniel H.T., E-mail: daniel.franco@ufv.b [Universidade Federal de Vicosa (UFV), Departamento de Fisica, Avenida Peter Henry Rolfs s/n, 36570-000, Vicosa, MG (Brazil); Piguet, Olivier, E-mail: opiguet@pq.cnpq.b [Universidade Federal do Espirito Santo (UFES), Departamento de Fisica, Campus Universitario de Goiabeiras, 29060-900, Vitoria, ES (Brazil)
2010-05-03
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field b, in the framework of algebraic renormalization - a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector b.
Lorentz and CPT violation in QED revisited: A missing analysis
International Nuclear Information System (INIS)
Del Cima, Oswaldo M.; Fonseca, Jakson M.; Franco, Daniel H.T.; Piguet, Olivier
2010-01-01
We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field b, in the framework of algebraic renormalization - a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector b.
Measurement of the Lorentz-FitzGerald body contraction
Rafelski, Johann
2018-02-01
A complete foundational discussion of acceleration in the context of Special Relativity (SR) is presented. Acceleration allows the measurement of a Lorentz-FitzGerald body contraction created. It is argued that in the back scattering of a probing laser beam from a relativistic flying electron cloud mirror generated by an ultra-intense laser pulse, a first measurement of a Lorentz-FitzGerald body contraction is feasible.
Non-Abelian Gauge Theory in the Lorentz Violating Background
Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais
2018-03-01
In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.
The BTZ black hole as a Lorentz-flat geometry
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Pedro D., E-mail: alvarez@physics.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, University of Oxford (United Kingdom); Pais, Pablo, E-mail: pais@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile); Rodríguez, Eduardo, E-mail: eduarodriguezsal@unal.edu.co [Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción (Chile); Salgado-Rebolledo, Patricio, E-mail: pasalgado@udec.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Zanelli, Jorge, E-mail: z@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile)
2014-11-10
It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.
Quantum-gravity phenomenology, Lorentz symmetry, and the SME
International Nuclear Information System (INIS)
Lehnert, Ralf
2007-01-01
Violations of spacetime symmetries have recently been identified as promising signatures for physics underlying the Standard Model. The present talk gives an overview over various topics in this field: The motivations for spacetime-symmetry research, including some mechanisms for Lorentz breaking, are reviewed. An effective field theory called the Standard-Model Extension (SME) for the description of the resulting low-energy effects is introduced, and some experimental tests of Lorentz and CPT invariance are discussed
A variational approach to closed bosonic strings on bordered Riemann surfaces
International Nuclear Information System (INIS)
Ohrndorf, T.
1987-01-01
Polyakov's path integral for bosonic closed strings defined on a bordered Riemann surface is investigated by variational methods. It is demonstrated that boundary variations are generated by the Virasoro operators. The investigation is performed for both, simply connected Riemann surfaces as well as ringlike domains. It is shown that the form of the variational operator is the same on both kinds of surfaces. The Virasoro algebra arises as a consistency condition for the variation. (orig.)
Probability laws related to the Jacobi theta and Riemann zeta function and Brownian excursions
Biane, P.; Pitman, J.; Yor, M.
1999-01-01
This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann's zeta function which are related to these laws.
Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.
Lorentz violation bounds from torsion trace fermion sector and galaxy M51 data and chiral dynamos
Energy Technology Data Exchange (ETDEWEB)
Garcia de Andrade, L.C. [IF-UERJ, Departamento de Fisica Teorica, Rio de Janeiro, RJ (Brazil)
2017-06-15
Earlier we have computed a Lorentz violation (LV) bound for torsion terms via galactic dynamos and found bounds similar to the one obtained by Kostelecky et al. (Phys Rev Lett 100:111102, 2008) which is of the order of 10{sup -31} GeV. Their result was found making use of the axial torsion vector in terms of Dirac spinors and minimal torsion coupling in flat space-time of fermions. In this paper, a torsion dynamo equation obtained using the variation of the torsion trace and galaxy M51 data of 500 pc are used to place an upper bound of 10{sup -26} GeV in LV, which agrees with the one by Kostelecky and his group using an astrophysical framework background. Their lowest bound was obtained in earth laboratory using dual masers. One of the purposes of this paper is to apply the Faraday self-induction magnetic equation, recently extended to torsioned space-time, by the author to show that it lends support to physics in Riemann-Cartan space-time, in several distinct physical backgrounds. Backreaction magnetic effects are used to obtain the LV bounds. Previously Bamba et al. (JCAP 10:058, 2012) have used the torsion trace in their teleparallel investigation of the IGMF, with the argument that the torsion trace leads to less weaker effects than the other irreducible components of the torsion tensor. LV is computed in terms of a chiral-torsion-like current in the new dynamo equation analogous to the Dvornikov and Semikoz dynamo equation with chiral magnetic currents. Making use of the chiral-torsion dynamo equation we estimate the LV bounds in the early universe to be of the order of 10{sup -24} GeV, which was the order of the charged-lepton sector. Our main result is that it is possible to obtain more stringent bounds than the ones found in the fermion sector of astrophysics in the new revised 2017 data table for CPT and Lorentz violation by Kostelecky and Mewes. They found in several astrophysical backgrounds, orders of magnitude such as 10{sup -24} and 10{sup -23} Ge
The Euler–Riemann gases, and partition identities
International Nuclear Information System (INIS)
Chair, Noureddine
2013-01-01
The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ 4 , and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t) 2 ) . Finally, we propose two formulas which brings
Hendrik Antoon Lorentz: his role in physics and society
Berends, Frits
2009-04-01
Hendrik Antoon Lorentz (1853-1928) was appointed in 1878 to a chair of theoretical physics at the University of Leiden, one of the first of such chairs in the world. A few years later Heike Kamerlingh Onnes became his experimental colleague, after vehement discussions in the faculty. Lorentz strongly supported Kamerlingh Onnes then, and proved subsequently to be an ideal colleague. With Lorentz's electron theory the classical theory of electromagnetism obtained its final form, at the time often called the Maxwell-Lorentz theory. In this theory the Zeeman effect could be explained: the first glimpse of the electron. The Nobel Prize followed in 1902. The Lorentz transformation, established in 1904, preceded the special theory of relativity. Later on, Lorentz played a much admired role in the debate on the new developments in physics, in particular as chairman of a series of Solvay conferences. Gradually his stature outside of physics grew, both nationally as chairman of the Zuiderzee committee and internationally as president of the International Commission on Intellectual Cooperation of the League of Nations. At his funeral the overwhelming tribute was the recognition of his unique greatness. Einstein said about him 'He meant more to me personally than anyone else I have met on my life's journey'.
Hendrik Antoon Lorentz: his role in physics and society
Energy Technology Data Exchange (ETDEWEB)
Berends, Frits [Emeritus Theoretical Physics, Leiden University (Netherlands)
2009-04-22
Hendrik Antoon Lorentz (1853-1928) was appointed in 1878 to a chair of theoretical physics at the University of Leiden, one of the first of such chairs in the world. A few years later Heike Kamerlingh Onnes became his experimental colleague, after vehement discussions in the faculty. Lorentz strongly supported Kamerlingh Onnes then, and proved subsequently to be an ideal colleague. With Lorentz's electron theory the classical theory of electromagnetism obtained its final form, at the time often called the Maxwell-Lorentz theory. In this theory the Zeeman effect could be explained: the first glimpse of the electron. The Nobel Prize followed in 1902. The Lorentz transformation, established in 1904, preceded the special theory of relativity. Later on, Lorentz played a much admired role in the debate on the new developments in physics, in particular as chairman of a series of Solvay conferences. Gradually his stature outside of physics grew, both nationally as chairman of the Zuiderzee committee and internationally as president of the International Commission on Intellectual Cooperation of the League of Nations. At his funeral the overwhelming tribute was the recognition of his unique greatness. Einstein said about him 'He meant more to me personally than anyone else I have met on my life's journey'.
Hendrik Antoon Lorentz: his role in physics and society
International Nuclear Information System (INIS)
Berends, Frits
2009-01-01
Hendrik Antoon Lorentz (1853-1928) was appointed in 1878 to a chair of theoretical physics at the University of Leiden, one of the first of such chairs in the world. A few years later Heike Kamerlingh Onnes became his experimental colleague, after vehement discussions in the faculty. Lorentz strongly supported Kamerlingh Onnes then, and proved subsequently to be an ideal colleague. With Lorentz's electron theory the classical theory of electromagnetism obtained its final form, at the time often called the Maxwell-Lorentz theory. In this theory the Zeeman effect could be explained: the first glimpse of the electron. The Nobel Prize followed in 1902. The Lorentz transformation, established in 1904, preceded the special theory of relativity. Later on, Lorentz played a much admired role in the debate on the new developments in physics, in particular as chairman of a series of Solvay conferences. Gradually his stature outside of physics grew, both nationally as chairman of the Zuiderzee committee and internationally as president of the International Commission on Intellectual Cooperation of the League of Nations. At his funeral the overwhelming tribute was the recognition of his unique greatness. Einstein said about him 'He meant more to me personally than anyone else I have met on my life's journey'.
The Lorentz-Dirac equation in light of quantum theory
International Nuclear Information System (INIS)
Nikishov, A.I.
1996-01-01
To high accuracy, an electron in ultrarelativistic motion 'sees' an external field in its rest frame as a crossed field (E=H, E·H=0). In this case, quantum expressions allow the introduction of a local intensity of the radiation, which determines the radiative term of the force of radiative reaction. For γ=(1-v2)-1/2>> 1 this term is much larger than the mass term, i.e., the term with xd3do. Under these conditions, the reduced Lorentz-Dirac equation, which is obtained from the full Lorentz-Dirac equation by eliminating the terms xd3do and xe on the right side using the equation of motion without taking into account the force of radiative reaction, is equivalent to good accuracy to the original Lorentz-Dirac equation. Exact solutions to the reduced Lorentz-Dirac equation are obtained for a constant field and the field of a plane wave. For γ∼1 a local expression for the radiative term cannot be obtained quantitatively from the quantum expressions. In this case the mass (Lorentz-Dirac) terms in the original and reduced Lorentz-Dirac equations are not small compared to the radiative term. The predictions of these equations, which depend appreciably on the mass terms, are therefore less reliable
Harmonic mappings into manifolds with boundary
International Nuclear Information System (INIS)
Chen Yunmei; Musina, R.
1989-08-01
In this paper we deal with harmonic maps from a compact Riemannian manifold into a manifold with boundary. In this case, a weak harmonic map is by definition a solution to a differential inclusion. In the first part of the paper we investigate the general properties of weak harmonic maps, which can be seen as solutions to a system of elliptic differential equations. In the second part we concentrate our attention on the heat flow method for harmonic maps. The result we achieve in this context extends a result by Chen and Struwe. (author). 21 refs
Manifolds for pose tracking from monocular video
Basu, Saurav; Poulin, Joshua; Acton, Scott T.
2015-03-01
We formulate a simple human-pose tracking theory from monocular video based on the fundamental relationship between changes in pose and image motion vectors. We investigate the natural embedding of the low-dimensional body pose space into a high-dimensional space of body configurations that behaves locally in a linear manner. The embedded manifold facilitates the decomposition of the image motion vectors into basis motion vector fields of the tangent space to the manifold. This approach benefits from the style invariance of image motion flow vectors, and experiments to validate the fundamental theory show reasonable accuracy (within 4.9 deg of the ground truth).
Effective Field Theory on Manifolds with Boundary
Albert, Benjamin I.
In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.
Matrix regularization of embedded 4-manifolds
International Nuclear Information System (INIS)
Trzetrzelewski, Maciej
2012-01-01
We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
Bernard, Julien
2018-02-01
I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.
Directory of Open Access Journals (Sweden)
K.J.B. Ghosh
2018-01-01
Full Text Available We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1 gauge fields Aμ(x which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension and have vanishing components A4(x (implying trivial holonomies in the 4-direction. Our calculation shows that the effective gauge-field action contains a local Chern–Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli–Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg–Wilson fermions.
Ghosh, K. J. B.; Klinkhamer, F. R.
2018-01-01
We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3 ×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U (1) gauge fields Aμ (x) which depend on all four spacetime coordinates (including the coordinate x4 ∈S1 of the compact dimension) and have vanishing components A4 (x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
La notion husserlienne de multiplicité : au-delà de Cantor et Riemann
Directory of Open Access Journals (Sweden)
Carlo Ierna
2012-04-01
Mannigfaltigkeit au sein de la pensée de Husserl (de ses débuts mathématiques jusqu’au rôle central qu’elle jouera plus tard à partir de l’arrière-fond et du contexte mathématique du développement de la philosophie de Husserl lui-même.The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of space. Husserl’s Mannigfaltigkeitslehre would then not be a Cantorian set-theory, but come rather closer to topology. Then, in the Prolegomena, Husserl introduces the idea of a pure Mannigfaltigkeitslehre as a meta-theoretical enterprise which studies the relations among theories, e.g. how to derive or found one upon another. When Husserl announces that in fact the best example of such a pure theory of manifolds is what is actually practiced in mathematics, this sounds slightly misleading. The pure theory of theories cannot simply be the mathematics underlying topology, but should rather be considered as a mathesis universalis. Indeed, while this might not have been fully clear yet in 1900/1901, Husserl will explicitly tie together the notions of pure theory of manifolds and mathesis universalis. The mathesis universalis in this sense is formal, a priori and analytic, as theory of theory in general. It is an analysis of the highest categories of meaning and their correlative categories of objects. In my paper I try to understand the development of the notion of Mannigfaltigkeit in Husserl’s thought from its mathematical beginnings to its later central philosophical role, taking into account the mathematical background and
Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods
International Nuclear Information System (INIS)
Ernst, Frederick J
2007-01-01
metric tensor components. The first two chapters of this book are devoted to some basic ideas: in the introductory chapter 1 the authors discuss the concept of integrability, comparing the integrability of the vacuum Ernst equation with the integrability of nonlinear equations of Korteweg-de Vries (KdV) type, while in chapter 2 they describe various circumstances in which the vacuum Ernst equation has been determined to be relevant, not only in connection with gravitation but also, for example, in the construction of solutions of the self-dual Yang-Mills equations. It is also in this chapter that one of several equivalent linear systems for the Ernst equation is described. The next two chapters are devoted to Dmitry Korotkin's concept of algebro-geometric solutions of a linear system: in chapter 3 the structure of such solutions of the vacuum Ernst equation, which involve Riemann theta functions of hyperelliptic algebraic curves of any genus, is contrasted with the periodic structure of such solutions of the KdV equation. How such solutions can be obtained, for example, by solving a matrix Riemann-Hilbert problem and how the metric tensor of the associated spacetime can be evaluated is described in detail. In chapter 4 the asymptotic behaviour and the similarity structure of the general algebro-geometric solutions of the Ernst equation are described, and the relationship of such solutions to the perhaps more familiar multi-soliton solutions is discussed. The next three chapters are based upon the authors' own published research: in chapter 5 it is shown that a problem involving counter-rotating infinitely thin disks of matter can be solved in terms of genus two Riemann theta functions, while in chapter 6 the authors describe numerical methods that facilitate the construction of such solutions, and in chapter 7 three-dimensional graphs are displayed that depict all metrical fields of the associated spacetime. Finally, in chapter 8, the difficulties associated with
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Minimal models on Riemann surfaces: The partition functions
International Nuclear Information System (INIS)
Foda, O.
1990-01-01
The Coulomb gas representation of the A n series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius) 2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)
Minimal models on Riemann surfaces: The partition functions
Energy Technology Data Exchange (ETDEWEB)
Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)
1990-06-04
The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).
Conformal fields. From Riemann surfaces to integrable hierarchies
International Nuclear Information System (INIS)
Semikhatov, A.M.
1991-01-01
I discuss the idea of translating ingredients of conformal field theory into the language of hierarchies of integrable differential equations. Primary conformal fields are mapped into (differential or matrix) operators living on the phase space of the hierarchy, whereas operator insertions of, e.g., a current or the energy-momentum tensor, become certain vector fields on the phase space and thus acquire a meaning independent of a given Riemann surface. A number of similarities are observed between the structures arising on the hierarchy and those of the theory on the world-sheet. In particular, there is an analogue of the operator product algebra with the Cauchy kernel replaced by its 'off-shell' hierarchy version. Also, hierarchy analogues of certain operator insertions admit two (equivalent, but distinct) forms, resembling the 'bosonized' and 'fermionized' versions respectively. As an application, I obtain a useful reformulation of the Virasoro constraints of the type that arise in matrix models, as a system of equations on dressing (or Lax) operators (rather than correlation functions, i.e., residues or traces). This also suggests an interpretation in terms of a 2D topological field theory, which might be extended to a correspondence between Virasoro-constrained hierarchies and topological theories. (orig.)
Numerical implication of Riemann problem theory for fluid dynamics
International Nuclear Information System (INIS)
Menikoff, R.
1988-01-01
The Riemann problem plays an important role in understanding the wave structure of fluid flow. It is also crucial step in some numerical algorithms for accurately and efficiently computing fluid flow; Godunov method, random choice method, and from tracking method. The standard wave structure consists of shock and rarefaction waves. Due to physical effects such as phase transitions, which often are indistinguishable from numerical errors in an equation of state, anomalkous waves may occur, ''rarefaction shocks'', split waves, and composites. The anomalous waves may appear in numerical calculations as waves smeared out by either too much artificial viscosity or insufficient resolution. In addition, the equation of state may lead to instabilities of fluid flow. Since these anomalous effects due to the equation of state occur for the continuum equations, they can be expected to occur for all computational algorithms. The equation of state may be characterized by three dimensionless variables: the adiabatic exponent γ, the Grueneisen coefficient Γ, and the fundamental derivative G. The fluid flow anomalies occur when inequalities relating these variables are violated. 18 refs
Deduction of Einstein equation from homogeneity of Riemann spacetime
Ni, Jun
2012-03-01
The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).
Four-manifolds, geometries and knots
Hillman, Jonathan A
2007-01-01
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery (Chapters 2-6), geometries and geometric decompositions (Chapters 7-13), and 2-knots (Chapters 14-18). In many cases the Euler characteristic, fundamental group and Stiefel-Whitney classes together form a complete system of invariants for the homotopy type of such manifolds, and the possible values of the invariants can be described explicitly. The strongest results are characterizations of manifolds which fibre homotopically over S^1 or an aspherical surface (up to homotopy equivalence) and infrasolvmanifolds (up to homeomorphism). As a consequence 2-knots whose groups are poly-Z are determined up to Gluck reconstruc...
International Nuclear Information System (INIS)
Becker, Katrin; Becker, Melanie; Robbins, Daniel
2015-01-01
In this talk we report on recent progress in describing compactifications of string theory and M-theory on G 2 and Spin(7) manifolds. We include the infinite set of α’-corrections and describe the entire tower of massless and massive Kaluza–Klein modes resulting from such compactifications. (invited comment)
The Koch curve as a smooth manifold
International Nuclear Information System (INIS)
Epstein, Marcelo; Sniatycki, Jedrzej
2008-01-01
We show that there exists a homeomorphism between the closed interval [0,1] is contained in R and the Koch curve endowed with the subset topology of R 2 . We use this homeomorphism to endow the Koch curve with the structure of a smooth manifold with boundary
Duality constructions from quantum state manifolds
Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.
2015-11-01
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Toric geometry of G2-manifolds
DEFF Research Database (Denmark)
Madsen, Thomas Bruun; Swann, Andrew Francis
We consider G2-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of T3-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz...
Conservative systems with ports on contact manifolds
Eberard, D.; Maschke, B.M.; van der Schaft, Arjan; Piztek, P.
In this paper we propose an extension of port Hamiltonian systems, called conservative systems with ports, which encompass systems arising from the Irreversible Thermodynamics. Firstly we lift a port Hamiltonian system from its state space manifold to the thermodynamic phase space to a contact
A generalized construction of mirror manifolds
International Nuclear Information System (INIS)
Berglund, P.; Huebsch, T.
1993-01-01
We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known. (orig.)
Foliations and the geometry of 3-manifolds
Calegari, Danny
2014-01-01
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions.
The structure of some classes of K-contact manifolds
Indian Academy of Sciences (India)
Abstract. We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi ...
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
Martínez-Torres, David; Miranda, Eva
2018-01-01
We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.
Hyperbolic manifolds as vacuum solutions in Kaluza-Klein theories
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1985-08-01
The relevance of compact hyperbolic manifolds in the context of Kaluza-Klein theories is discussed. Examples of spontaneous compactification on hyperbolic manifolds including d dimensional (d>=8) Einstein-Yang-Mills gravity and 11-dimensional supergravity are considered. Some mathematical facts about hyperbolic manifolds essential for the physical content of the theory are briefly summarized. Non-linear σ-models based on hyperbolic manifolds are discussed. (author)
Fluid manifold design for a solar energy storage tank
Humphries, W. R.; Hewitt, H. C.; Griggs, E. I.
1975-01-01
A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.
Some theorems on a class of harmonic manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Chen Weihuan.
1993-08-01
A class of harmonic n-manifold, denoted by HM n , is, in fact, focussed on a Riemannian manifold with harmonic curvature. A variety of results, with properties, on HM n is presented in a fair order. Harmonic manifolds are then touched upon manifolds with recurrent Ricci curvature, biRicci-recurrent curvature and recurrent conformal curvature, and, in consequence, a sequence of theorems are deduced. (author). 21 refs
LORENTZ PHASE IMAGING AND IN-SITU LORENTZ MICROSCOPY OF PATTERNED CO-ARRAYS
International Nuclear Information System (INIS)
VOLKOV, V.V.; ZHU, Y.
2003-01-01
Understanding magnetic structures and properties of patterned and ordinary magnetic films at nanometer length-scale is the area of immense technological and fundamental scientific importance. The key feature to such success is the ability to achieve visual quantitative information on domain configurations with a maximum ''magnetic'' resolution. Several methods have been developed to meet these demands (Kerr and Faraday effects, differential phase contrast microscopy, magnetic force microscopy, SEMPA etc.). In particular, the modern off-axis electron holography allows retrieval of the electron-wave phase shifts down to 2π/N (with typical N = 10-20, approaching in the limit N ∼ 100) in TEM equipped with field emission gun, which is already successfully employed for studies of magnetic materials at nanometer scale. However, it remains technically demanding, sensitive to noise and needs highly coherent electron sources. As possible alternative we developed a new method of Lorentz phase microscopy [1,2] based on the Fourier solution [3] of magnetic transport-of-intensity (MTIE) equation. This approach has certain advantages, since it is less sensitive to noise and does not need high coherence of the source required by the holography. In addition, it can be realized in any TEM without basic hardware changes. Our approach considers the electron-wave refraction in magnetic materials (magnetic refraction) and became possible due to general progress in understanding of noninterferometric phase retrieval [4-6] dealing with optical refraction. This approach can also be treated as further development of Fresnel microscopy, used so far for imaging of in-situ magnetization process in magnetic materials studied by TEM. Figs. 1-3 show some examples of what kind information can be retrieved from the conventional Fresnel images using the new approach. Most of these results can be compared with electron-holographic data. Using this approach we can shed more light on fine details of
A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
Baker, Mark; Cooper, Daryl
2005-01-01
We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, there are finite index subgroups which generate a subgroup that is an amalgamated free product. Constructions of infinite volume hyperbolic n-manifolds are described by gluing lo...
Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds
Indian Academy of Sciences (India)
We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...
Higher-order Jordan Osserman pseudo-Riemannian manifolds
International Nuclear Information System (INIS)
Gilkey, Peter B; Ivanova, Raina; Zhang Tan
2002-01-01
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds
Higher-order Jordan Osserman pseudo-Riemannian manifolds
Energy Technology Data Exchange (ETDEWEB)
Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)
2002-09-07
We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-11-01
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.
In-depth Study on Cylinder Wake Controlled by Lorentz Force
International Nuclear Information System (INIS)
Zhang Hui; Fan Bao-Chun; Chen Zhi-Hua
2011-01-01
The underlying mechanisms of the electromagnetic control of cylinder wake are investigated and discussed. The effects of Lorentz force are found to be composed of two parts, one is its direct action on the cylinder (the wall Lorentz force) and the other is applied to the fluid (called the field Lorentz force) near the cylinder surface. Our results show that the wall Lorentz force can generate thrust and reduce the drag; the field Lorentz force increases the drag. However, the cylinder drag is dominated by the wall Lorentz force. In addition, the field Lorentz force above the upper surface decreases the lift, while the upper wall Lorentz force increases it. The total lift is dominated by the upper wall Lorentz force. (fundamental areas of phenomenology(including applications))
A Polyakov action on Riemann surfaces. Pt. 2
International Nuclear Information System (INIS)
Zucchini, R.
1991-11-01
The model independent study of the Polyakov action is continued on an arbitrary compact surface without boundary of genus larger than 2 as the general solution of the relevant conformal Ward identity. A general formula for the Polyakov action and an explicit calculation of the energy-momentum tensor density is provided. The general geometric setting of the construction is described in detail. It is shown that the Polyakov action defines a distribution of finite dimensional directions in the holomorphic tangent bundle of the manifold of Beltrami differentials. It is further argued that motions parallel to such distribution correspond to Polyakov's SL(2,C) symmetry transformations. Owing to the existence of renormalization ambiguities on a topologically non-trivial surface, the energy-momentum tensor needs not be invariant under the full SL(2,C) symmetry. The residual SL(2,C) symmetry is characterized geometrically. (author) 31 refs
Lorentz Violation of the Photon Sector in Field Theory Models
Directory of Open Access Journals (Sweden)
Lingli Zhou
2014-01-01
Full Text Available We compare the Lorentz violation terms of the pure photon sector between two field theory models, namely, the minimal standard model extension (SME and the standard model supplement (SMS. From the requirement of the identity of the intersection for the two models, we find that the free photon sector of the SMS can be a subset of the photon sector of the minimal SME. We not only obtain some relations between the SME parameters but also get some constraints on the SMS parameters from the SME parameters. The CPT-odd coefficients (kAFα of the SME are predicted to be zero. There are 15 degrees of freedom in the Lorentz violation matrix Δαβ of free photons of the SMS related with the same number of degrees of freedom in the tensor coefficients (kFαβμν, which are independent from each other in the minimal SME but are interrelated in the intersection of the SMS and the minimal SME. With the related degrees of freedom, we obtain the conservative constraints (2σ on the elements of the photon Lorentz violation matrix. The detailed structure of the photon Lorentz violation matrix suggests some applications to the Lorentz violation experiments for photons.
On the ether-like Lorentz-breaking actions
International Nuclear Information System (INIS)
Petrov, A.Yu; Nascimento, J.R.; Gomes, M.; Silva, A. J. da
2011-01-01
We demonstrate the generation of the CPT-even, ether-like Lorentz-breaking actions for the scalar and electro-magnetic fields via their appropriate Lorentz-breaking coupling to spinor fields in three, four and five space-time dimensions. Besides, we show that the ether-like terms for the spinor field also can be generated as a consequence of the same couplings. The key result which will be presented here is the finiteness of the ether-like term for the electromagnetic field not only in three and five space-time dimensions where it is natural due to known effects of the dimensional regularization but also in four space-time dimensions. Moreover, we present the calculation of the last result within different calculational schemes and conclude that the result for the four-dimensional ether-like term for the electromagnetic field essentially depending on the calculation scheme, similarly to the result for the Carroll-Field-Jackiw (CFJ) term which probably signalizes a possibility for arising of a new anomaly. Also we discuss the dispersion relations in the theories with ether-like Lorentz-breaking terms which allows to discuss the consistency of the Lorentz-breaking modified theories for different (space-like or time-like) Lorentz-breaking vectors and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the action of the scalar field. (author)
Lorentz-violating alternative to the Higgs mechanism?
International Nuclear Information System (INIS)
Alexandre, Jean; Mavromatos, Nick E.
2011-01-01
We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavor mixing, and to another Abelian vector field with flavor mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale M, from which fermions and the flavor-mixing vector get their dynamical masses, whereas the vector coupled without flavor mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, while the vector mass is of the order of the heavy fermion mass. The work presented here may be considered as a Lorentz-symmetry-violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz violation, the maximal (light-cone) speed seen by the fermions is smaller than that of the massless gauge boson (which equals the speed of light in vacuo) by an amount which is unacceptably large to be compatible with the current tests of Lorentz invariance, unless the gauge couplings assume unnaturally small values. Possible ways out of this phenomenological drawback are briefly discussed, postponing a detailed construction of more realistic models for future work.
Lorentz-violating theories in the standard model extension
Energy Technology Data Exchange (ETDEWEB)
Ferreira Junior, Manoel Messias [Universidade Federal do Maranhao (UFMA), Sao Luis, MA (Brazil)
2012-07-01
Full text: Lorentz-violating theories have been an issue of permanent interest in the latest years. Many of these investigations are developed under the theoretical framework of the Standard Model Extension (SME), a broad extension of the minimal Standard Model embracing Lorentz-violating (LV) terms, generated as vacuum expectation values of tensor quantities, in all sectors of interaction. In this talk, we comment on some general properties of the SME, concerning mainly the gauge and fermion sectors, focusing in new phenomena induced by Lorentz violation. The LV terms are usually separated in accordance with the behavior under discrete symmetries, being classified as CPT-odd or CPT-even, parity-even or parity-odd. We follow this classification scheme discussing some features and new properties of the CPT-even and CPT-odd parts of the gauge and fermion sectors. We finalize presenting some upper bounds imposed on the corresponding LV coefficients. (author)
Lorentz violation and black-hole thermodynamics: Compton scattering process
International Nuclear Information System (INIS)
Kant, E.; Klinkhamer, F.R.; Schreck, M.
2009-01-01
A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentz-violating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the mass of the black hole, is found to have a nonzero probability. These events perhaps allow for a violation of the generalized second law of thermodynamics in the Lorentz-noninvariant theory considered.
Special Relativity in Week One: 3) Introducing the Lorentz Contraction
Huggins, Elisha
2011-05-01
This is the third of four articles on teaching special relativity in the first week of an introductory physics course.1,2 With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie "Time Dilation, an Experiment with Mu-Mesons" by David Frisch and James Smith.3,4 The movie demonstrates that time dilation and the Lorentz contraction are essentially two sides of the same coin. Here we take the muon's point of view for a more intuitive understanding of the Lorentz contraction, and use the results of the movie to provide an insight into the way we interpret experimental results involving special relativity.
Comment on 'Lorentz transformations with arbitrary line of motion'
International Nuclear Information System (INIS)
Tjiang, Paulus C; Sutanto, Sylvia H
2007-01-01
A short comment regarding the derivation of Lorentz transformation proposed by Iyer and Prabhu (2007 Eur. J. Phys. 11 183-90) is given. It is shown that the proposed derivation is similar to that appearing in the standard textbooks of classical mechanics, electrodynamics and the theory of relativity. In fact, those textbooks also provide an elegant form of the Lorentz matrix for the (3+1)-dimensional case, which Iyer and Prabhu claim to be difficult to attain because of its algebraic complexity. We also provide the derivation of the (3+1)-dimensional version of the Lorentz matrix using a method analogous to that proposed by Iyer and Prabhu, and show that the result is completely equivalent to the (3+1)-dimensional version appearing in the textbooks. (letters and comments)
Convexity and concavity constants in Lorentz and Marcinkiewicz spaces
Kaminska, Anna; Parrish, Anca M.
2008-07-01
We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].
Detecting Lorentz Violations with Gravitational Waves From Black Hole Binaries
Sotiriou, Thomas P.
2018-01-01
Gravitational wave observations have been used to test Lorentz symmetry by looking for dispersive effects that are caused by higher order corrections to the dispersion relation. In this Letter I argue on general grounds that, when such corrections are present, there will also be a scalar excitation. Hence, a smoking-gun observation of Lorentz symmetry breaking would be the direct detection of scalar waves that travel at a speed other than the speed of the standard gravitational wave polarizations or the speed of light. Interestingly, in known Lorentz-breaking gravity theories the difference between the speeds of scalar and tensor waves is virtually unconstrained, whereas the difference between the latter and the speed of light is already severely constrained by the coincident detection of gravitational waves and gamma rays from a binary neutron star merger.
Topological quantum field theory and four manifolds
Marino, Marcos
2005-01-01
The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...
Modular categories and 3-manifold invariants
International Nuclear Information System (INIS)
Tureav, V.G.
1992-01-01
The aim of this paper is to give a concise introduction to the theory of knot invariants and 3-manifold invariants which generalize the Jones polynomial and which may be considered as a mathematical version of the Witten invariants. Such a theory was introduced by N. Reshetikhin and the author on the ground of the theory of quantum groups. here we use more general algebraic objects, specifically, ribbon and modular categories. Such categories in particular arise as the categories of representations of quantum groups. The notion of modular category, interesting in itself, is closely related to the notion of modular tensor category in the sense of G. Moore and N. Seiberg. For simplicity we restrict ourselves in this paper to the case of closed 3-manifolds
Echocardiogram enhancement using supervised manifold denoising.
Wu, Hui; Huynh, Toan T; Souvenir, Richard
2015-08-01
This paper presents data-driven methods for echocardiogram enhancement. Existing denoising algorithms typically rely on a single noise model, and do not generalize to the composite noise sources typically found in real-world echocardiograms. Our methods leverage the low-dimensional intrinsic structure of echocardiogram videos. We assume that echocardiogram images are noisy samples from an underlying manifold parametrized by cardiac motion and denoise images via back-projection onto a learned (non-linear) manifold. Our methods incorporate synchronized side information (e.g., electrocardiography), which is often collected alongside the visual data. We evaluate the proposed methods on a synthetic data set and real-world echocardiograms. Quantitative results show improved performance of our methods over recent image despeckling methods and video denoising methods, and a visual analysis of real-world data shows noticeable image enhancement, even in the challenging case of noise due to dropout artifacts. Copyright © 2015 Elsevier B.V. All rights reserved.
Topological anomalies for Seifert 3-manifolds
Energy Technology Data Exchange (ETDEWEB)
Imbimbo, Camillo [Dipartimento di Fisica, Università di Genova,Via Dodecaneso 33, 16146 Genova (Italy); INFN - Sezione di Genova,Via Dodecaneso 33, 16146, Genova (Italy); Rosa, Dario [School of Physics and Astronomy andCenter for Theoretical Physics Seoul National University,Seoul 151-747 (Korea, Republic of); Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN - Sezione di Milano-Bicocca,I-20126 Milano (Italy)
2015-07-14
We study globally supersymmetric 3d gauge theories on curved manifolds by describing the coupling of 3d topological gauge theories, with both Yang-Mills and Chern-Simons terms in the action, to background topological gravity. In our approach, the Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the BRST transformations of topological gravity. A cohomological characterization of the geometrical moduli which affect the partition function is obtained. In the Seifert context the Chern-Simons topological (framing) anomaly is BRST trivial. We compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of 3d supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.
Dynamical systems on 2- and 3-manifolds
Grines, Viacheslav Z; Pochinka, Olga V
2016-01-01
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed. < The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are present...
Convex nonnegative matrix factorization with manifold regularization.
Hu, Wenjun; Choi, Kup-Sze; Wang, Peiliang; Jiang, Yunliang; Wang, Shitong
2015-03-01
Nonnegative Matrix Factorization (NMF) has been extensively applied in many areas, including computer vision, pattern recognition, text mining, and signal processing. However, nonnegative entries are usually required for the data matrix in NMF, which limits its application. Besides, while the basis and encoding vectors obtained by NMF can represent the original data in low dimension, the representations do not always reflect the intrinsic geometric structure embedded in the data. Motivated by manifold learning and Convex NMF (CNMF), we propose a novel matrix factorization method called Graph Regularized and Convex Nonnegative Matrix Factorization (GCNMF) by introducing a graph regularized term into CNMF. The proposed matrix factorization technique not only inherits the intrinsic low-dimensional manifold structure, but also allows the processing of mixed-sign data matrix. Clustering experiments on nonnegative and mixed-sign real-world data sets are conducted to demonstrate the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.
Synchronizing and controlling hyperchaos in complex Lorentz-Haken systems
Energy Technology Data Exchange (ETDEWEB)
Jinqing, Fang [Academia Sinica, Beijing, BJ (China). Inst. of Atomic Energy
1995-03-01
Synchronizing hyperchaos is realized by the drive-response relationship in the complex Lorentz-Haken system and its higher-order cascading systems for the first time. Controlling hyperchaos is achieved by the intermittent proportional feedback to all of the drive (master) system variables. The complex Lorentz-Haken system describes the detuned single-mode laser and is taken as a typical example of hyperchaotic synchronization to clarify our ideas and results. The ideas and concepts could be extended to some nonlinear dynamical systems and have prospects for potential applications, for example. to laser, electronics, plasma, cryptography, communication, chemical and biological systems and so on. (8 figs., 2 tabs.).
Synchronizing and controlling hyperchaos in complex Lorentz-Haken systems
International Nuclear Information System (INIS)
Fang Jinqing
1995-03-01
Synchronizing hyperchaos is realized by the drive-response relationship in the complex Lorentz-Haken system and its higher-order cascading systems for the first time. Controlling hyperchaos is achieved by the intermittent proportional feedback to all of the drive (master) system variables. The complex Lorentz-Haken system describes the detuned single-mode laser and is taken as a typical example of hyperchaotic synchronization to clarify our ideas and results. The ideas and concepts could be extended to some nonlinear dynamical systems and have prospects for potential applications, for example. to laser, electronics, plasma, cryptography, communication, chemical and biological systems and so on. (8 figs., 2 tabs.)
Lorentz and CPT violation in the Standard-Model Extension
Energy Technology Data Exchange (ETDEWEB)
Lehnert, Ralf, E-mail: ralehner@indiana.edu [Indiana University Center for Spacetime Symmetries (United States)
2013-03-15
Lorentz and CPT invariance are among the symmetries that can be investigated with ultrahigh precision in subatomic physics. Being spacetime symmetries, Lorentz and CPT invariance can be violated by minuscule amounts in many theoretical approaches to underlying physics that involve novel spacetime concepts, such as quantized versions of gravity. Regardless of the underlying mechanism, the low-energy effects of such violations are expected to be governed by effective field theory. This talk provides a survey of this idea and includes an overview of experimental efforts in the field.
Lorentz and Poincaré invariance 100 years of relativity
Hsu Jong Ping
2001-01-01
This collection of papers provides a broad view of the development of Lorentz and Poincaré invariance and spacetime symmetry throughout the past 100 years. The issues explored in these papers include: (1) formulations of relativity theories in which the speed of light is not a universal constant but which are consistent with the four-dimensional symmetry of the Lorentz and Poincaré groups and with experimental results, (2) analyses and discussions by Reichenbach concerning the concepts of simultaneity and physical time from a philosophical point of view, and (3) results achieved by the union o
Sasakian manifolds with purely transversal Bach tensor
Ghosh, Amalendu; Sharma, Ramesh
2017-10-01
We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2 n (2 n +1 ) , equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).
CFD simulations for engine intake manifolds
International Nuclear Information System (INIS)
Witry, A.; Zhao, A.
2002-01-01
This paper attempts to explain a procedure for using Computational Fluid Dynamics (CFD) for product development of engine intake manifolds. The paper uses the development of an intake manifold as an example of such a process. Using the commercial FLUENT solver, its standard wall functions and k-ε model, a four runner intake manifold with an average mesh size of 300, 000 hexa elements created in ICEM-CFD with a maximum skewness of 0.85 produces rapid results for quick product turn-around times. The setup used allows for compressibility and viscous heating effects to be modeled whilst ignoring wall heat transfer due to the high speeds of the air/foil mixture and low residence times. Eight consecutive models were modeled here whilst carrying out continuous enhancements. For every iteration, four different so called 'static' runs with only one runner open at any one time using a steady state assumption were calculated further assuming that only one intake valve is open at any one time. Even flow distributions between the runner are deemed to be 'dynamically' obtained once the pressure drops between the manifold's inlet and runner outlets are equalized. Furthermore, different modifications were attempted to ensure that the fluid's particle tracks show very little particle return tendencies along with excellent nonuniformity indexes at the runners outlets. Confirmation of these results were obtained from test data showing CFD pressure drop predictions to be within 4% error with 67% of any runner's pressure losses being caused in the runner itself due to the small cross sectional area(s). (author)
Fine topology and locally Minkowskian manifolds
Agrawal, Gunjan; Sinha, Soami Pyari
2018-05-01
Fine topology is one of the several well-known topologies of physical and mathematical relevance. In the present paper, it is obtained that the nonempty open sets of different dimensional Minkowski spaces with the fine topology are not homeomorphic. This leads to the introduction of a new class of manifolds. It turns out that the technique developed here is also applicable to some other topologies, namely, the s-topology, space topology, f-topology, and A-topology.
On complete manifolds supporting a weighted Sobolev type inequality
International Nuclear Information System (INIS)
Adriano, Levi; Xia Changyu
2011-01-01
Highlights: → We study manifolds supporting a weighted Sobolev or log-Sobolev inequality. → We investigate manifolds of asymptotically non-negative Ricci curvature. → The constant in the weighted Sobolev inequality on complete manifolds is studied. - Abstract: This paper studies the geometric and topological properties of complete open Riemannian manifolds which support a weighted Sobolev or log-Sobolev inequality. We show that the constant in the weighted Sobolev inequality on a complete open Riemannian manifold should be bigger than or equal to the optimal one on the Euclidean space of the same dimension and that a complete open manifold of asymptotically non-negative Ricci curvature supporting a weighted Sobolev inequality must have large volume growth. We also show that a complete manifold of non-negative Ricci curvature on which the log-Sobolev inequality holds is not very far from the Euclidean space.
Sasaki-Einstein Manifolds and Volume Minimisation
Martelli, D; Yau, S T; Martelli, Dario; Sparks, James; Yau, Shing-Tung
2006-01-01
We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theo...
Manifold learning in machine vision and robotics
Bernstein, Alexander
2017-02-01
Smart algorithms are used in Machine vision and Robotics to organize or extract high-level information from the available data. Nowadays, Machine learning is an essential and ubiquitous tool to automate extraction patterns or regularities from data (images in Machine vision; camera, laser, and sonar sensors data in Robotics) in order to solve various subject-oriented tasks such as understanding and classification of images content, navigation of mobile autonomous robot in uncertain environments, robot manipulation in medical robotics and computer-assisted surgery, and other. Usually such data have high dimensionality, however, due to various dependencies between their components and constraints caused by physical reasons, all "feasible and usable data" occupy only a very small part in high dimensional "observation space" with smaller intrinsic dimensionality. Generally accepted model of such data is manifold model in accordance with which the data lie on or near an unknown manifold (surface) of lower dimensionality embedded in an ambient high dimensional observation space; real-world high-dimensional data obtained from "natural" sources meet, as a rule, this model. The use of Manifold learning technique in Machine vision and Robotics, which discovers a low-dimensional structure of high dimensional data and results in effective algorithms for solving of a large number of various subject-oriented tasks, is the content of the conference plenary speech some topics of which are in the paper.
Quantized Dirac field in curved Riemann--Cartan background. I. Symmetry properties, Green's function
International Nuclear Information System (INIS)
Nieh, H.T.; Yan, M.L.
1982-01-01
In the present series of papers, we study the properties of quantized Dirac field in curved Riemann--Cartan space, with particular attention on the role played by torsion. In this paper, we give, in the spirit of the original work of Weyl, a systematic presentation of Dirac's theory in curved Riemann--Cartan space. We discuss symmetry properties of the system, and derive conservation laws as direct consequences of these symmetries. Also discussed is conformal gauge symmetry, with torsion effectively playing the role of a conformal gauge field. To obtain short-distance behavior, we calculate the spinor Green's function, in curved Riemann--Cartan background, using the Schwinger--DeWitt method of proper-time expansion. The calculation corresponds to a generalization of DeWitt's calculation for a Riemannian background
International Nuclear Information System (INIS)
Zolotarev, Vladimir A
2009-01-01
Functional models are constructed for commutative systems {A 1 ,A 2 } of bounded linear non-self-adjoint operators which do not contain dissipative operators (which means that ξ 1 A 1 +ξ 2 A 2 is not a dissipative operator for any ξ 1 , ξ 2 element of R). A significant role is played here by the de Branges transform and the function classes occurring in this context. Classes of commutative systems of operators {A 1 ,A 2 } for which such a construction is possible are distinguished. Realizations of functional models in special spaces of meromorphic functions on Riemann surfaces are found, which lead to reasonable analogues of de Branges spaces on these Riemann surfaces. It turns out that the functions E(p) and E-tilde(p) determining the order of growth in de Branges spaces on Riemann surfaces coincide with the well-known Baker-Akhiezer functions. Bibliography: 11 titles.
Explicit solution of Riemann-Hilbert problems for the Ernst equation
Klein, C.; Richter, O.
1998-01-01
Riemann-Hilbert problems are an important solution technique for completely integrable differential equations. They are used to introduce a free function in the solutions which can be used at least in principle to solve initial or boundary value problems. But even if the initial or boundary data can be translated into a Riemann-Hilbert problem, it is in general impossible to obtain explicit solutions. In the case of the Ernst equation, however, this is possible for a large class because the matrix problem can be shown to be gauge equivalent to a scalar one on a hyperelliptic Riemann surface that can be solved in terms of theta functions. As an example we discuss the rigidly rotating dust disk.
Four-dimensional aether-like Lorentz-breaking QED revisited and problem of ambiguities
Energy Technology Data Exchange (ETDEWEB)
Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Rua Hugo D' Antola, 95, Lapa, Sao Paulo (Brazil); Mariz, T. [Universidade Federal de Alagoas, Instituto de Fisica, Maceio, Alagoas (Brazil); Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica, Caixa Postal 5008, Joao Pessoa, Paraiba (Brazil)
2013-08-15
In this paper, we consider the perturbative generation of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED within different approaches and discuss its ambiguities. (orig.)
Four-dimensional aether-like Lorentz-breaking QED revisited and problem of ambiguities
International Nuclear Information System (INIS)
Baeta Scarpelli, A.P.; Mariz, T.; Nascimento, J.R.; Petrov, A.Yu.
2013-01-01
In this paper, we consider the perturbative generation of the CPT-even aether-like Lorentz-breaking term in the extended Lorentz-breaking QED within different approaches and discuss its ambiguities. (orig.)
Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
Chiodaroli, Elisabetta; Kreml, Ondřej
2018-04-01
We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.
SO(N) WZNW models on higher-genus Riemann surfaces
International Nuclear Information System (INIS)
Alimohammadi, M.; Arfaei, H.; Bonn Univ.
1993-08-01
With the help of the string functions and fusion rules of SO(2N) 1 , we show that the results on SU(N) 1 correlators on higher-genus Riemann surfaces (HGRS) can be extended to the SO(2N) 1 and other level-one simply-laced WZNW models. Using modular invariance and factorization properties of Green functions we find multipoint correlators of primary and descendant fields of SO(2N+1) 1 WZNW models on higher genus Riemann surfaces. (orig.)
Modular transformations of conformal blocks in WZW models on Riemann surfaces of higher genus
International Nuclear Information System (INIS)
Miao Li; Ming Yu.
1989-05-01
We derive the modular transformations for conformal blocks in Wess-Zumino-Witten models on Riemann surfaces of higher genus. The basic ingredient consists of using the Chern-Simons theory developed by Witten. We find that the modular transformations generated by Dehn twists are linear combinations of Wilson line operators, which can be expressed in terms of braiding matrices. It can also be shown that modular transformation matrices for g > 0 Riemann surfaces depend only on those for g ≤ 3. (author). 13 refs, 15 figs
Ghil, M.; Balgovind, R.
1979-01-01
The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.
Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies
Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul
2018-03-01
This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.
Reassessing Riemann's paper on the number of primes less than a given magnitude
Dittrich, Walter
2018-01-01
In this book, the author pays tribute to Bernhard Riemann (1826–1866), mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. This book concentrates in particular on Riemann’s only work on prime numbers, including such then new ideas as analytical continuation in the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta function is presented. The impact of Riemann’s ideas on regularizing infinite values in field theory is also emphasized.
Riemann problems and their application to ultra-relativistic heavy ion collisions
International Nuclear Information System (INIS)
Plohr, B.J.; Sharp, D.H.
1986-07-01
Heavy ion collisions at sufficiently high energies to form quark-gluon plasma are considered. The phase transformation from a quark-gluon phase to hadrons as the nuclear matter cools is modeled as a hydrodynamical flow. Nonlinear waves are the predominant feature of this type of flow and the Riemann problem of a relativistic gas undergoing a phase transformation is explored as a method to numerically model this phase transition process in nuclear matter. The solution of the Riemann problem is outlined and results of preliminary numerical computations of the flow are presented. 10 refs., 2 figs
Local Extrema of the $\\Xi(t)$ Function and The Riemann Hypothesis
Kobayashi, Hisashi
2016-01-01
In the present paper we obtain a necessary and sufficient condition to prove the Riemann hypothesis in terms of certain properties of local extrema of the function $\\Xi(t)=\\xi(\\tfrac{1}{2}+it)$. First, we prove that positivity of all local maxima and negativity of all local minima of $\\Xi(t)$ form a necessary condition for the Riemann hypothesis to be true. After showing that any extremum point of $\\Xi(t)$ is a saddle point of the function $\\Re\\{\\xi(s)\\}$, we prove that the above properties o...
Reduction of 4-dim self dual super Yang-Mills onto super Riemann surfaces
International Nuclear Information System (INIS)
Mendoza, A.; Restuccia, A.; Martin, I.
1990-05-01
Recently self dual super Yang-Mills over a super Riemann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of 4-dim Euclidean self dual super Yang-Mills in terms of constraints on the supercurvature. By dimensional reduction we obtain the same set of superconformal field equations which define self dual connections on a super Riemann surface. (author). 10 refs
Direct observation of rectified motion of vortices by Lorentz microscopy
Indian Academy of Sciences (India)
We have investigated the vortex dynamics for the `ratchet' operation in a niobium superconductor via a direct imaging of Lorentz microscopy. We directly observe one-directional selective motion of field-gradient-driven vortices along fabricated channels. This results from the rectification of vortices in a spatially asymmetric ...
Studying Lorentz-violating electromagnetic waves in confined media
International Nuclear Information System (INIS)
Viana, Davidson R.; Gomes, Andre H.; Fonseca, Jakson M.; Moura-Melo, Winder A.
2009-01-01
Full text. Planck energy scale is still far beyond current possibilities. A question of interest is whether the Lorentz symmetry remains valid at these extremely high energies, whose answer certainly would be useful whenever building grand unified theories, in which general relativity is consistently accommodated. Here, we study a reminiscent of this possible symmetry violation, incorporated in the body of the so-called Standard Model Extension (SME). More precisely, we deal with the pure (Abelian) gauge sector, so that we have a modified classical electromagnetism in (3+1) dimensions, whose Lagrangian include a term proportional to a (constant) background tensor that breaks the Lorentz symmetry, but respecting CPT. Our attention is devoted to the wave-like solutions constrained to propagate inside confined media, like waveguides and resonant cavities. Our preliminary findings indicate that Lorentz-breaking implies in modifications of the standard results which are proportional to the (very small) violating parameters, but could be largely enhanced by diminishing the size of the confined media. Under study is the case of a toroidal cavity where the electromagnetic field should respect the additional requirement of being single-valued in the (toroidal) angular variable. Perhaps, such an extra feature combined with the usual boundary conditions could lead us to large effects of this violation, somewhat similar to those predicted for CPT- and Lorentz-odd electromagnetic waves constrained to propagate along a hollow conductor waveguide. (author)
On Einstein's kinematics and his derivation of Lorentz transformation equations
International Nuclear Information System (INIS)
Gulati, Shobha; Gulati, S.P.
1981-01-01
Recently the present authors have claimed that Einstein's historic derivation of 1905 of Lorentz transformation equations is a 'howler' - a correct result achieved through some incorrect steps. In the present contribution, this howler is fully resolved. Incidently, Einstein's kinematical considerations are found to be void of any new definitional elements or conventionality as unjustifiably claimed by Einstein and some other scientists. (author)
Lorentz- and CPT-symmetry studies in subatomic physics
Energy Technology Data Exchange (ETDEWEB)
Lehnert, Ralf, E-mail: ralehner@indiana.edu [Leibniz Universität Hannover (Germany)
2016-12-15
Subatomic systems provide an exquisite test bench for spacetime symmetries. This work motivates such measurements, reviews the effective field theory test framework for the description of Lorentz and CPT violation, and employs this framework to study the phenomenology of spacetime-symmetry breaking in various subatomic systems.
On the Lorentz degree of a product of polynomials
Ait-Haddou, Rachid
2015-01-01
In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.
The scientific correspondence of H. A. Lorentz: Volume I
Kox, A.J.
2008-01-01
This book presents a selection of 434 carefully annotated letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death in February 1928. Most of these letters are of a scientific nature, with the
Structural aspects of Lorentz-violating quantum field theory
Cambiaso, M.; Lehnert, R.; Potting, R.
2018-01-01
In the last couple of decades the Standard Model Extension has emerged as a fruitful framework to analyze the empirical and theoretical extent of the validity of cornerstones of modern particle physics, namely, of Special Relativity and of the discrete symmetries C, P and T (or some combinations of these). The Standard Model Extension allows to contrast high-precision experimental tests with posited alterations representing minute Lorentz and/or CPT violations. To date no violation of these symmetry principles has been observed in experiments, mostly prompted by the Standard-Model Extension. From the latter, bounds on the extent of departures from Lorentz and CPT symmetries can be obtained with ever increasing accuracy. These analyses have been mostly focused on tree-level processes. In this presentation I would like to comment on structural aspects of perturbative Lorentz violating quantum field theory. I will show that some insight coming from radiative corrections demands a careful reassessment of perturbation theory. Specifically I will argue that both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted given that the asymptotic single-particle states can receive quantum corrections from Lorentz-violating operators that are not present in the original Lagrangian.
A Lorentz-Violating Alternative to Higgs Mechanism?
Alexandre, Jean
2011-01-01
We consider a four-dimensional field-theory model with two massless fermions, coupled to an Abelian vector field without flavour mixing, and to another Abelian vector field with flavour mixing. Both Abelian vectors have a Lorentz-violating kinetic term, introducing a Lorentz-violation mass scale $M$, from which fermions and the flavour-mixing vector get their dynamical masses, whereas the vector coupled without flavour mixing remains massless. When the two coupling constants have similar values in order of magnitude, a mass hierarchy pattern emerges, in which one fermion is very light compared to the other, whilst the vector mass is larger than the mass of the heavy fermion. The work presented here may be considered as a Lorentz-symmetry-Violating alternative to the Higgs mechanism, in the sense that no scalar particle (fundamental or composite) is necessary for the generation of the vector-meson mass. However, the model is not realistic given that, as a result of Lorentz Violation, the maximal (light-cone) s...
Lorentz force actuation of a heated atomic force microscope cantilever.
Lee, Byeonghee; Prater, Craig B; King, William P
2012-02-10
We report Lorentz force-induced actuation of a silicon microcantilever having an integrated resistive heater. Oscillating current through the cantilever interacts with the magnetic field around a NdFeB permanent magnet and induces a Lorentz force that deflects the cantilever. The same current induces cantilever heating. With AC currents as low as 0.2 mA, the cantilever can be oscillated as much as 80 nm at resonance with a DC temperature rise of less than 5 °C. By comparison, the AC temperature variation leads to a thermomechanical oscillation that is about 1000 times smaller than the Lorentz deflection at the cantilever resonance. The cantilever position in the nonuniform magnetic field affects the Lorentz force-induced deflection, with the magnetic field parallel to the cantilever having the largest effect on cantilever actuation. We demonstrate how the cantilever actuation can be used for imaging, and for measuring the local material softening temperature by sensing the contact resonance shift.
Anomalous current in periodic Lorentz gases with infinite horizon
Energy Technology Data Exchange (ETDEWEB)
Dolgopyat, Dmitrii I [University of Maryland, College Park (United States); Chernov, Nikolai I [University of Alabama at Birmingham, Birmingham, Alabama (United States)
2009-08-31
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
Anomalous current in periodic Lorentz gases with infinite horizon
International Nuclear Information System (INIS)
Dolgopyat, Dmitrii I; Chernov, Nikolai I
2009-01-01
Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, that is, J=1/2 D*E+o(||E||), where D* is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by J=1/2 DE| log||E|| | + O(||E||), where D is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju. Bibliography: 31 titles.
On the Lorentz degree of a product of polynomials
Ait-Haddou, Rachid
2015-01-01
In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence
A note on Lorentz transformation and pseudo-rapidity distributions
International Nuclear Information System (INIS)
Hama, Y.
1980-07-01
It is shown that although rapidity and pseudo-rapidity are almost equivalent variables, their difference may in pratice become quite remarkable. Non Lorentz invariance of pseudo-rapidity distributions may cause appearance of strange effects at first sight, such as deformation of a perfectly symmetric particle distribution into an asymmetric one when going to another frame. (Author) [pt
Adaptive compensation of Lorentz force detuning in superconducting RF cavities
Energy Technology Data Exchange (ETDEWEB)
Pischalnikov, Yuriy [Fermilab; Schappert, Warren [Fermilab
2011-11-01
The Lorentz force can dynamically detune pulsed Superconducting RF cavities and considerable additional RF power can be required to maintain the accelerating gradient if no effort is made to compensate. Fermilab has developed an adaptive compensation system for cavities in the Horizontal Test Stand, in the SRF Accelerator Test Facility, and for the proposed Project X.
Prospects for Lorentz and CPT tests with hydrogen and antihydrogen
Becker, Tobias Frederic
2017-01-01
As a summer student for 13 weeks in the ASACUSA-CUSP collaboration, under the supervision of Chloé Malbrunot, my project consisted in a first part on the theoretical treatment of Lorentz and CPT violation in hydrogen & antihydrogen in the framework of the Standard Model Extension SME and in second part on experimental measurements on a hydrogen beam.
What Governs Lorentz Factors of Jet Components in Blazars? Xinwu ...
Indian Academy of Sciences (India)
Abstract. We use a sample of radio-loud Active Galactic Nuclei. (AGNs) with measured black hole masses to explore the jet formation mechanisms in these sources. We find a significant correlation between black hole mass and the bulk Lorentz factor of the jet components for this sample, while no significant correlation is ...
What Governs Lorentz Factors of Jet Components in Blazars?
Indian Academy of Sciences (India)
We use a sample of radio-loud Active Galactic Nuclei (AGNs) with measured black hole masses to explore the jet formation mechanisms in these sources. We find a significant correlation between black hole mass and the bulk Lorentz factor of the jet components for this sample, while no significant correlation is present ...
Helicity and evanescent waves. [Energy transport velocity, helicity, Lorentz transformation
Energy Technology Data Exchange (ETDEWEB)
Agudin, J L; Platzeck, A M [La Plata Univ. Nacional (Argentina); Albano, J R [Instituto de Astronomia y Fisica del Espacio, Buenos Aires, Argentina
1978-02-20
It is shown that the projection of the angular momentum of a circularly polarized electromagnetic evanescent wave along the mean velocity of energy transport (=helicity) can be reverted by a Lorentz transformation, in spite of the fact that this velocity is c.
Black holes in Lorentz-violating gravity theories
International Nuclear Information System (INIS)
Barausse, Enrico; Sotiriou, Thomas P
2013-01-01
Lorentz symmetry and the notion of light cones play a central role in the definition of horizons and the existence of black holes. Current observations provide strong indications that astrophysical black holes do exist in Nature. Here we explore what happens to the notion of a black hole in gravity theories where local Lorentz symmetry is violated, and discuss the relevant astrophysical implications. Einstein-aether theory and Hořava gravity are used as the theoretical background for addressing this question. We review earlier results about static, spherically symmetric black holes, which demonstrate that in Lorentz-violating theories there can be a new type of horizon and, hence, a new notion of black hole. We also present both known and new results on slowly rotating black holes in these theories, which provide insights on how generic these new horizons are. Finally, we discuss the differences between black holes in Lorentz-violating theories and in General Relativity, and assess to what extent they can be probed with present and future observations. (paper)
Special Relativity in Week One: 3) Introducing the Lorentz Contraction
Huggins, Elisha
2011-01-01
This is the third of four articles on teaching special relativity in the first week of an introductory physics course. With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie…
Cosmic rays and the search for a Lorentz Invariance Violation
International Nuclear Information System (INIS)
Bietenholz, Wolfgang
2008-11-01
This is an introductory review about the on-going search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultra high energy (UHECRs). We discuss the Greisen-Zatsepin-Kuz'min (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even at factors γ ∝ O(10 11 ). For heavier nuclei the energy attenuation is even faster due to photo-disintegration, again if this process is Lorentz invariant. Hence the viability of Lorentz symmetry up to tremendous γ-factors - far beyond accelerator tests - is a central issue. Next we comment on conceptual aspects of Lorentz Invariance and the possibility of its spontaneous breaking. This could lead to slightly particle dependent ''Maximal Attainable Velocities''. We discuss their effect in decays, Cerenkov radiation, the GZK cutoff and neutrino oscillation in cosmic rays. We also review the search for LIV in cosmic γ-rays. For multi TeV γ-rays we possibly encounter another puzzle related to the transparency of the CMB, similar to the GZK cutoff, due to electron/positron creation and subsequent inverse Compton scattering. The photons emitted in a Gamma Ray Burst occur at lower energies, but their very long path provides access to information not far from the Planck scale. We discuss conceivable non-linear photon dispersions based on non-commutative geometry or effective approaches. No LIV has been observed so far. However, even extremely tiny LIV effects could change the predictions for cosmic ray physics drastically. An Appendix is devoted to the recent hypothesis by the Pierre Auger Collaboration, which identifies nearby Active Galactic Nuclei - or objects next to them - as probable UHECR sources. (orig.)
Monoids of moduli spaces of manifolds
DEFF Research Database (Denmark)
Galatius, Søren; Randal-Williams, Oscar
2010-01-01
We study categories of d–dimensional cobordisms from the perspective of Tillmann [Invent. Math. 130 (1997) 257–275] and Galatius, Madsen, Tillman and Weiss [Acta Math. 202 (2009) 195–239]. There is a category C¿ of closed smooth (d - 1)–manifolds and smooth d–dimensional cobordisms, equipped...... with generalised orientations specified by a map ¿: X ¿ BO(d). The main result of [Acta Math. 202 (2009) 195–239] is a determination of the homotopy type of the classifying space BC¿. The goal of the present paper is a systematic investigation of subcategories D¿C¿ with the property that BD¿ BC¿, the smaller...
Manifold structure preservative for hyperspectral target detection
Imani, Maryam
2018-05-01
A nonparametric method termed as manifold structure preservative (MSP) is proposed in this paper for hyperspectral target detection. MSP transforms the feature space of data to maximize the separation between target and background signals. Moreover, it minimizes the reconstruction error of targets and preserves the topological structure of data in the projected feature space. MSP does not need to consider any distribution for target and background data. So, it can achieve accurate results in real scenarios due to avoiding unreliable assumptions. The proposed MSP detector is compared to several popular detectors and the experiments on a synthetic data and two real hyperspectral images indicate the superior ability of it in target detection.
Rational Homological Stability for Automorphisms of Manifolds
DEFF Research Database (Denmark)
Grey, Matthias
In this thesis we prove rational homological stability for the classifying spaces of the homotopy automorphisms and block di↵eomorphisms of iterated connected sums of products of spheres of a certain connectivity.The results in particular apply to the manifolds Npg,q = (#g(Sp x Sq)) - int...... with coefficients in the homology of the universal covering, which is studied using rational homology theory. The result for the block di↵eomorphisms is deduced from the homological stability for the homotopy automorphisms upon using Surgery theory. Themain theorems of this thesis extend the homological stability...
Laplacian embedded regression for scalable manifold regularization.
Chen, Lin; Tsang, Ivor W; Xu, Dong
2012-06-01
Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real
Super-quasi-conformal transformation and Schiffer variation on super-Riemann surface
International Nuclear Information System (INIS)
Takahasi, Wataru
1990-01-01
A set of equations which characterizes the super-Teichmueller deformations is proposed. It is a supersymmetric extension of the Beltrami equation. Relations between the set of equations and the Schiffer variations with the KN bases are discussed. This application of the KN bases shows the powerfulness of the KN theory in the study of super-Riemann surfaces. (author)
The Great Gorilla Jump: An Introduction to Riemann Sums and Definite Integrals
Sealey, Vicki; Engelke, Nicole
2012-01-01
The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…
Riemann type algebraic structures and their differential-algebraic integrability analysis
Directory of Open Access Journals (Sweden)
Prykarpatsky A.K.
2010-06-01
Full Text Available The differential-algebraic approach to studying the Lax type integrability of generalized Riemann type equations is devised. The differentiations and the associated invariant differential ideals are analyzed in detail. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.
Infinite conformal symmetries and Riemann-Hilbert transformation in super principal chiral model
International Nuclear Information System (INIS)
Hao Sanru; Li Wei
1989-01-01
This paper shows a new symmetric transformation - C transformation in super principal chiral model and discover an infinite dimensional Lie algebra related to the Virasoro algebra without central extension. By using the Riemann-Hilbert transformation, the physical origination of C transformation is discussed
International Nuclear Information System (INIS)
Wang Shikun; Xu Kaiwen.
1989-12-01
The superconformal algebras of meromorphic vector fields with multipoles, the central extension and the relevant abelian differential of the third kind on super Riemann sphere were constructed. The background of our theory is concerned with the interaction of closed superstrings. (author). 9 refs
Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
Bender, Carl M.; Brody, Dorje C.
2018-04-01
The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.
International Nuclear Information System (INIS)
Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.
1984-09-01
The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)
Representation theory of current algebra and conformal field theory on Riemann surfaces
International Nuclear Information System (INIS)
Yamada, Yasuhiko
1989-01-01
We study conformal field theories with current algebra (WZW-model) on general Riemann surfaces based on the integrable representation theory of current algebra. The space of chiral conformal blocks defined as solutions of current and conformal Ward identities is shown to be finite dimensional and satisfies the factorization properties. (author)
International Nuclear Information System (INIS)
Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.
1995-01-01
The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented
Moser, Jan
2015-01-01
In this paper we introduce complicated oscillating system, namely quotient of two multiforms based on Riemann-Siegel formula. We prove that there is an infinite set of metamorphoses of this system (=chrysalis) on critical line $\\sigma=\\frac 12$ into a butterfly (=infinite series of M\\" obius functions in the region of absolute convergence $\\sigma>1$).
Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)
International Nuclear Information System (INIS)
Shen Jianmin; Sheng Zhengmao; Wang Zhonghua
1992-02-01
We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs
Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere
International Nuclear Information System (INIS)
Sabbah, C
2004-01-01
It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin
Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds
Weeks, Jeffrey R.
2005-01-01
Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary tetrahedral space S3/T*, the prism manifolds S3/D...
Strong Proximities on Smooth Manifolds and Vorono\\" i Diagrams
Peters, J. F.; Guadagni, C.
2015-01-01
This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proxim...
Some problems of dynamical systems on three dimensional manifolds
International Nuclear Information System (INIS)
Dong Zhenxie.
1985-08-01
It is important to study the dynamical systems on 3-dimensional manifolds, its importance is showing up in its close relation with our life. Because of the complication of topological structure of Dynamical systems on 3-dimensional manifolds, generally speaking, the search for 3-dynamical systems is not easier than 2-dynamical systems. This paper is a summary of the partial result of dynamical systems on 3-dimensional manifolds. (author)
Total Generalized Variation for Manifold-valued Data
Bredies, K.; Holler, M.; Storath, M.; Weinmann, A.
2017-01-01
In this paper we introduce the notion of second-order total generalized variation (TGV) regularization for manifold-valued data. We provide an axiomatic approach to formalize reasonable generalizations of TGV to the manifold setting and present two possible concrete instances that fulfill the proposed axioms. We provide well-posedness results and present algorithms for a numerical realization of these generalizations to the manifold setup. Further, we provide experimental results for syntheti...
CT Image Reconstruction in a Low Dimensional Manifold
Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie
2017-01-01
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...
On the trace-manifold generated by the deformations of a body-manifold
Directory of Open Access Journals (Sweden)
Boja Nicolae
2003-01-01
Full Text Available In this paper, concerned to the study of continuous deformations of material media using some tools of modem differential geometry, a moving frame of Frenet type along the orbits of an one-parameter group acting on a so-called "trace-manifold", M, associated to the deformations, is constructed. The manifold M is defined as an infinite union of non-disjoint compact manifolds, generated by the consecutive positions in the Euclidean affine 3-space of a body-manifold under deformations in a closed time interval. We put in evidence a skew-symmetric band tensor of second order, ω, which describes the deformation in a small neighborhood of any point along the orbits. The non-null components ωi,i+i, (i =1,2, of ω are assimilated as like curvatures at each point of an orbit in the planes generated by the pairs of vectors (ĕi,ĕi+i of a moving frame in M associated to the orbit in a similar way as the Frenet's frame is. Also a formula for the energy of the orbits is given and its relationship with some stiffness matrices is established.
LCD OF AIR INTAKE MANIFOLDS PHASE 2: FORD F250 AIR INTAKE MANIFOLD
The life cycle design methodology was applied to the design analysis of three alternatives for the lower plehum of the air intake manifold for us with a 5.4L F-250 truck engine: a sand cast aluminum, a lost core molded nylon composite, and a vibration welded nylon composite. The ...
Variable area manifolds for ring mirror heat exchangers
Eng, Albert; Senterfitt, Donald R.
1988-05-01
A laser ring mirror assembly is disclosed which supports and cools an annular ring mirror of a high powered laser with a cooling manifold which has a coolant flow design which is intended to reduce thermal distortions of the ring mirror by minimizing azimuthal variations in temperature around its circumference. The cooling manifold has complementary pairs of cooling passages each of which conduct coolant in opposite flow directions. The manifold also houses adjusters which vary the depth between the annular ring mirror and each cooling, and which vary the flow area of the cooling passage to produce a control over the cooling characteristics of the cooling manifold.
Totally Contact Umbilical Lightlike Hypersurfaces of Indefinite -Manifolds
Directory of Open Access Journals (Sweden)
Rachna Rani
2013-01-01
Full Text Available We study totally contact umbilical lightlike hypersurfaces of indefinite -manifolds and prove the nonexistence of totally contact umbilical lightlike hypersurface in indefinite -space form.
Efficient orbit integration by manifold correction methods.
Fukushima, Toshio
2005-12-01
Triggered by a desire to investigate, numerically, the planetary precession through a long-term numerical integration of the solar system, we developed a new formulation of numerical integration of orbital motion named manifold correct on methods. The main trick is to rigorously retain the consistency of physical relations, such as the orbital energy, the orbital angular momentum, or the Laplace integral, of a binary subsystem. This maintenance is done by applying a correction to the integrated variables at each integration step. Typical methods of correction are certain geometric transformations, such as spatial scaling and spatial rotation, which are commonly used in the comparison of reference frames, or mathematically reasonable operations, such as modularization of angle variables into the standard domain [-pi, pi). The form of the manifold correction methods finally evolved are the orbital longitude methods, which enable us to conduct an extremely precise integration of orbital motions. In unperturbed orbits, the integration errors are suppressed at the machine epsilon level for an indefinitely long period. In perturbed cases, on the other hand, the errors initially grow in proportion to the square root of time and then increase more rapidly, the onset of which depends on the type and magnitude of the perturbations. This feature is also realized for highly eccentric orbits by applying the same idea as used in KS-regularization. In particular, the introduction of time elements greatly enhances the performance of numerical integration of KS-regularized orbits, whether the scaling is applied or not.
Manifold-Based Visual Object Counting.
Wang, Yi; Zou, Yuexian; Wang, Wenwu
2018-07-01
Visual object counting (VOC) is an emerging area in computer vision which aims to estimate the number of objects of interest in a given image or video. Recently, object density based estimation method is shown to be promising for object counting as well as rough instance localization. However, the performance of this method tends to degrade when dealing with new objects and scenes. To address this limitation, we propose a manifold-based method for visual object counting (M-VOC), based on the manifold assumption that similar image patches share similar object densities. Firstly, the local geometry of a given image patch is represented linearly by its neighbors using a predefined patch training set, and the object density of this given image patch is reconstructed by preserving the local geometry using locally linear embedding. To improve the characterization of local geometry, additional constraints such as sparsity and non-negativity are also considered via regularization, nonlinear mapping, and kernel trick. Compared with the state-of-the-art VOC methods, our proposed M-VOC methods achieve competitive performance on seven benchmark datasets. Experiments verify that the proposed M-VOC methods have several favorable properties, such as robustness to the variation in the size of training dataset and image resolution, as often encountered in real-world VOC applications.
Lagrangian descriptors of driven chemical reaction manifolds.
Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto
2017-08-01
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
How (not) to teach Lorentz covariance of the Dirac equation
International Nuclear Information System (INIS)
Nikolić, Hrvoje
2014-01-01
In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties. (paper)
Testing Lorentz invariance of dark matter with satellite galaxies
Energy Technology Data Exchange (ETDEWEB)
Bettoni, Dario [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Nusser, Adi [Physics Department and the Asher Space Science Institute—Technion, Haifa 32000 (Israel); Blas, Diego; Sibiryakov, Sergey, E-mail: d.bettoni@thphys.uni-heidelberg.de, E-mail: adi@physics.technion.ac.il, E-mail: diego.blas@cern.ch, E-mail: sergey.sibiryakov@cern.ch [Theoretical Physics Department, CERN, CH-1211 Geneva 23 (Switzerland)
2017-05-01
We develop the framework for testing Lorentz invariance in the dark matter sector using galactic dynamics. We consider a Lorentz violating (LV) vector field acting on the dark matter component of a satellite galaxy orbiting in a host halo. We introduce a numerical model for the dynamics of satellites in a galactic halo and for a galaxy in a rich cluster to explore observational consequences of such an LV field. The orbital motion of a satellite excites a time dependent LV force which greatly affects its internal dynamics. Our analysis points out key observational signatures which serve as probes of LV forces. These include modifications to the line of sight velocity dispersion, mass profiles and shapes of satellites. With future data and a more detailed modeling these signatures can be exploited to constrain a new region of the parameter space describing the LV in the dark matter sector.
Linear negative magnetoresistance in two-dimensional Lorentz gases
Schluck, J.; Hund, M.; Heckenthaler, T.; Heinzel, T.; Siboni, N. H.; Horbach, J.; Pierz, K.; Schumacher, H. W.; Kazazis, D.; Gennser, U.; Mailly, D.
2018-03-01
Two-dimensional Lorentz gases formed by obstacles in the shape of circles, squares, and retroreflectors are reported to show a pronounced linear negative magnetoresistance at small magnetic fields. For circular obstacles at low number densities, our results agree with the predictions of a model based on classical retroreflection. In extension to the existing theoretical models, we find that the normalized magnetoresistance slope depends on the obstacle shape and increases as the number density of the obstacles is increased. The peaks are furthermore suppressed by in-plane magnetic fields as well as by elevated temperatures. These results suggest that classical retroreflection can form a significant contribution to the magnetoresistivity of two-dimensional Lorentz gases, while contributions from weak localization cannot be excluded, in particular for large obstacle densities.
Lorentz covariance ‘almost’ implies electromagnetism and more
International Nuclear Information System (INIS)
Sobouti, Y
2015-01-01
Beginning from two simple assumptions, (i) the speed of light is a universal constant, or its equivalent, the spacetime intervals are Lorentz invariant, and (ii) there are mutually interacting particles, with a covariant ‘source-field’ equation, one arrives at a class of field equations of which the standard electromagnetism (EM) and electrodynamics are special cases. The formalism, depending on how one formulates the source-field equation, allows one to speculate magnetic monopoles, massive photons, nonlinear EMs, and more. (paper)
Unified derivation of the Galileo and the Lorentz transformations
International Nuclear Information System (INIS)
Sardelis, D.A.
1982-01-01
By using the principle of relativity together with the general assumptions of space-time homogeneity and space isotropy underlying the principle of inertia, a most general transformation is constructed connecting any two inertial frames. The Galileo and the Lorentz transformations are then deduced by constraining these general inertial transformations through the corresponding two physical principles: the (classical) principle of acceleration invariance and the (relativistic) principle that all interactions propagate with the same finite and invariant speed. (author)
Control of weakly conductive fluids by near wall Lorentz forces
Energy Technology Data Exchange (ETDEWEB)
Hinze, M. [Technische Univ. Dresden (Germany). Inst. fuer Numerische Mathematik
2007-07-01
In this work optimal and model-predictive control approaches for control of weakly conductive fluids are developed. The flow around the circular cylinder at low Reynolds numbers serves as prototyping application. Control by near-wall Lorentz forces gains either to suppress the formation of the von Karman Vortex Street, or to reduce the drag. Besides a concise mathematical modelling numerical examples are presented which highlight the scope of the presented control approaches. (orig.)
Characterization of associate spaces of weighted Lorentz spaces with applications
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Pick, L.; Soudský, F.
2014-01-01
Roč. 224, č. 1 (2014), s. 1-23 ISSN 0039-3223 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : weighted Lorentz spaces * weighted inequalities * non-increasing rearragement * Banach function space Subject RIV: BA - General Mathematics Impact factor: 0.610, year: 2014 http://journals.impan.gov.pl/sm/Inf/224-1-1.html
Heat conduction in caricature models of the Lorentz gas
International Nuclear Information System (INIS)
Kramli, A.; Simanyi, N.; Szasz, D.
1987-01-01
Heat transport coefficients are calculated for various random walks with internal states (the Markov partition of the Sinai billiard connects these walks with the Lorentz gas among a periodic configuration of scatterers). Models with reflecting or absorbing barriers and also those without or with local thermal equilibrium are investigated. The method is unified and is based on the Keldysh expansion of the resolvent of a matrix polynomial
Embeddings of Lorentz-type spaces involving weighted integral means
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Křepela, M.; Pick, L.; Soudský, F.
2017-01-01
Roč. 273, č. 9 (2017), s. 2939-2980 ISSN 0022-1236 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : classical Lorentz spaces * embeddings * iterated operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.254, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022123617302252
Prospects for testing Lorentz and CPT symmetry with antiprotons
Vargas, Arnaldo J.
2018-03-01
A brief overview of the prospects of testing Lorentz and CPT symmetry with antimatter experiments is presented. The models discussed are applicable to atomic spectroscopy experiments, Penning-trap experiments and gravitational tests. Comments about the sensitivity of the most recent antimatter experiments to the models reviewed here are included. This article is part of the Theo Murphy meeting issue `Antiproton physics in the ELENA era'.
Prospects for testing Lorentz and CPT symmetry with antiprotons.
Vargas, Arnaldo J
2018-03-28
A brief overview of the prospects of testing Lorentz and CPT symmetry with antimatter experiments is presented. The models discussed are applicable to atomic spectroscopy experiments, Penning-trap experiments and gravitational tests. Comments about the sensitivity of the most recent antimatter experiments to the models reviewed here are included.This article is part of the Theo Murphy meeting issue 'Antiproton physics in the ELENA era'. © 2018 The Author(s).
Directory of Open Access Journals (Sweden)
Meina Sun
2016-05-01
Full Text Available We study the Riemann problem for a non-strictly hyperbolic system of conservation laws under the linear approximations of flux functions with three parameters. The approximated system also belongs to the type of triangular systems of conservation laws and this approximation does not change the structure of Riemann solutions to the original system. Furthermore, it is proven that the Riemann solutions to the approximated system converge to the corresponding ones to the original system as the perturbation parameter tends to zero.
Comment on self-inverse form of the Lorentz transformation
International Nuclear Information System (INIS)
Cook, R.J.
1979-01-01
It has been shown that the kinematic relations between two iertial reference frames in relative motion can be made symmetric by an appropriate orientation of the coordinate axes of the two frames. It follows from this symmetry and the principle of relativity that the transformation matrix, A, from one frame to the other, and its inverse, A -1 , are equal. This result, along with a limiting-velocity postulate, was used in a derivation of the Lorentz transformation. The present note points out that only two transformation laws are compatible with the symmetry condition A = A -1 . One of these is the Lorentz transformation and the other violates causality. Thus, if the limiting-velocity postulate is replaced by the requirement that causality be satisfied in all inertial frames, one arrives at a derivation of the Lorentz transformation based entirely on concepts which were known and widely accepted long before the advent of special relativity: the homogeneity and isotropy of space in all inertial frames, the principle of relativity, and the principle of causality
Remote sub-wavelength focusing of ultrasonically activated Lorentz current
Rekhi, Angad S.; Arbabian, Amin
2017-04-01
We propose the use of a combination of ultrasonic and magnetic fields in conductive media for the creation of RF electrical current via the Lorentz force, in order to achieve current generation with extreme sub-wavelength resolution at large depth. We demonstrate the modeling, generation, and measurement of Lorentz current in a conductive solution and show that this current can be localized at a distance of 13 cm from the ultrasonic source to a region about three orders of magnitude smaller than the corresponding wavelength of electromagnetic waves at the same operation frequency. Our results exhibit greater depth, tighter localization, and closer agreement with prediction than previous work on the measurement of Lorentz current in a solution of homogeneous conductivity. The proposed method of RF current excitation overcomes the trade-off between focusing and propagation that is fundamental in the use of RF electromagnetic excitation alone and has the potential to improve localization and depth of operation for RF current-based biomedical applications.
Manifold corrections on spinning compact binaries
International Nuclear Information System (INIS)
Zhong Shuangying; Wu Xin
2010-01-01
This paper deals mainly with a discussion of three new manifold correction methods and three existing ones, which can numerically preserve or correct all integrals in the conservative post-Newtonian Hamiltonian formulation of spinning compact binaries. Two of them are listed here. One is a new momentum-position scaling scheme for complete consistency of both the total energy and the magnitude of the total angular momentum, and the other is the Nacozy's approach with least-squares correction of the four integrals including the total energy and the total angular momentum vector. The post-Newtonian contributions, the spin effects, and the classification of orbits play an important role in the effectiveness of these six manifold corrections. They are all nearly equivalent to correct the integrals at the level of the machine epsilon for the pure Kepler problem. Once the third-order post-Newtonian contributions are added to the pure orbital part, three of these corrections have only minor effects on controlling the errors of these integrals. When the spin effects are also included, the effectiveness of the Nacozy's approach becomes further weakened, and even gets useless for the chaotic case. In all cases tested, the new momentum-position scaling scheme always shows the optimal performance. It requires a little but not much expensive additional computational cost when the spin effects exist and several time-saving techniques are used. As an interesting case, the efficiency of the correction to chaotic eccentric orbits is generally better than one to quasicircular regular orbits. Besides this, the corrected fast Lyapunov indicators and Lyapunov exponents of chaotic eccentric orbits are large as compared with the uncorrected counterparts. The amplification is a true expression of the original dynamical behavior. With the aid of both the manifold correction added to a certain low-order integration algorithm as a fast and high-precision device and the fast Lyapunov
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J. M.
2008-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Conformal Vector Fields on Doubly Warped Product Manifolds and Applications
Directory of Open Access Journals (Sweden)
H. K. El-Sayied
2016-01-01
Full Text Available This article aimed to study and explore conformal vector fields on doubly warped product manifolds as well as on doubly warped spacetime. Then we derive sufficient conditions for matter and Ricci collineations on doubly warped product manifolds. A special attention is paid to concurrent vector fields. Finally, Ricci solitons on doubly warped product spacetime admitting conformal vector fields are considered.
The quantum equivariant cohomology of toric manifolds through mirror symmetry
Baptista, J.M.
2009-01-01
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.
Variable volume combustor with nested fuel manifold system
McConnaughhay, Johnie Franklin; Keener, Christopher Paul; Johnson, Thomas Edward; Ostebee, Heath Michael
2016-09-13
The present application provides a combustor for use with a gas turbine engine. The combustor may include a number of micro-mixer fuel nozzles, a fuel manifold system in communication with the micro-mixer fuel nozzles to deliver a flow of fuel thereto, and a linear actuator to maneuver the micro-mixer fuel nozzles and the fuel manifold system.
Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds
Yaning Wang; Ximin Liu
2012-01-01
We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Contact manifolds, Lagrangian Grassmannians and PDEs
Directory of Open Access Journals (Sweden)
Eshkobilov Olimjon
2018-02-01
Full Text Available In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.. As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
Evolutionary global optimization, manifolds and applications
Aguiar e Oliveira Junior, Hime
2016-01-01
This book presents powerful techniques for solving global optimization problems on manifolds by means of evolutionary algorithms, and shows in practice how these techniques can be applied to solve real-world problems. It describes recent findings and well-known key facts in general and differential topology, revisiting them all in the context of application to current optimization problems. Special emphasis is put on game theory problems. Here, these problems are reformulated as constrained global optimization tasks and solved with the help of Fuzzy ASA. In addition, more abstract examples, including minimizations of well-known functions, are also included. Although the Fuzzy ASA approach has been chosen as the main optimizing paradigm, the book suggests that other metaheuristic methods could be used as well. Some of them are introduced, together with their advantages and disadvantages. Readers should possess some knowledge of linear algebra, and of basic concepts of numerical analysis and probability theory....
Transition Manifolds of Complex Metastable Systems
Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof
2018-04-01
We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.
Manifold Adaptive Label Propagation for Face Clustering.
Pei, Xiaobing; Lyu, Zehua; Chen, Changqing; Chen, Chuanbo
2015-08-01
In this paper, a novel label propagation (LP) method is presented, called the manifold adaptive label propagation (MALP) method, which is to extend original LP by integrating sparse representation constraint into regularization framework of LP method. Similar to most LP, first of all, MALP also finds graph edges from given data and gives weights to the graph edges. Our goal is to find graph weights matrix adaptively. The key advantage of our approach is that MALP simultaneously finds graph weights matrix and predicts the label of unlabeled data. This paper also derives efficient algorithm to solve the proposed problem. Extensions of our MALP in kernel space and robust version are presented. The proposed method has been applied to the problem of semi-supervised face clustering using the well-known ORL, Yale, extended YaleB, and PIE datasets. Our experimental evaluations show the effectiveness of our method.
Directory of Open Access Journals (Sweden)
Kyncl Martin
2017-01-01
Full Text Available We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side. The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy, therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some
Cosmic rays and the search for a Lorentz Invariance Violation
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang, E-mail: wolbi@nucleares.unam.mx
2011-08-15
This is an introductory review about the ongoing search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultrahigh energy (UHECRs). We discuss the Greisen-Zatsepin-Kuz'min (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even at factors {gamma}{approx}O(10{sup 11}). For heavier nuclei, the energy attenuation is even faster due to photo-disintegration, again if this process is Lorentz invariant. Hence the viability of Lorentz symmetry up to tremendous {gamma}-factors-far beyond accelerator tests-is a central issue. Next, we comment on conceptual aspects of Lorentz Invariance and the possibility of its spontaneous breaking. This could lead to slightly particle dependent 'Maximal Attainable Velocities'. We discuss their effect in decays, Cerenkov radiation, the GZK cutoff and neutrino oscillation in cosmic rays. We also review the search for LIV in cosmic {gamma}-rays. For multi-TeV {gamma}-rays, we encounter another possible puzzle related to the transparency of the CMB, similar to the GZK cutoff, due to electron/positron creation and subsequent inverse Compton scattering. The photons emitted in a Gamma Ray Burst occur at lower energies, but their very long path provides access to information not that far from the Planck scale. We discuss conceivable nonlinear photon dispersions based on non-commutative geometry or effective approaches. No LIV has been observed so far. However, even extremely tiny LIV effects could change the predictions for cosmic ray physics drastically. An Appendix is devoted to the recent results by the Pierre Auger Collaboration, in particular the hypothesis that nearby Active Galactic Nuclei-or objects next to
Cosmic rays and the search for a Lorentz Invariance Violation
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2008-11-15
This is an introductory review about the on-going search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultra high energy (UHECRs). We discuss the Greisen-Zatsepin-Kuz'min (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even at factors {gamma} {proportional_to} O(10{sup 11}). For heavier nuclei the energy attenuation is even faster due to photo-disintegration, again if this process is Lorentz invariant. Hence the viability of Lorentz symmetry up to tremendous {gamma}-factors - far beyond accelerator tests - is a central issue. Next we comment on conceptual aspects of Lorentz Invariance and the possibility of its spontaneous breaking. This could lead to slightly particle dependent ''Maximal Attainable Velocities''. We discuss their effect in decays, Cerenkov radiation, the GZK cutoff and neutrino oscillation in cosmic rays. We also review the search for LIV in cosmic {gamma}-rays. For multi TeV {gamma}-rays we possibly encounter another puzzle related to the transparency of the CMB, similar to the GZK cutoff, due to electron/positron creation and subsequent inverse Compton scattering. The photons emitted in a Gamma Ray Burst occur at lower energies, but their very long path provides access to information not far from the Planck scale. We discuss conceivable non-linear photon dispersions based on non-commutative geometry or effective approaches. No LIV has been observed so far. However, even extremely tiny LIV effects could change the predictions for cosmic ray physics drastically. An Appendix is devoted to the recent hypothesis by the Pierre Auger Collaboration, which identifies nearby Active Galactic Nuclei - or objects
Model Transport: Towards Scalable Transfer Learning on Manifolds
DEFF Research Database (Denmark)
Freifeld, Oren; Hauberg, Søren; Black, Michael J.
2014-01-01
We consider the intersection of two research fields: transfer learning and statistics on manifolds. In particular, we consider, for manifold-valued data, transfer learning of tangent-space models such as Gaussians distributions, PCA, regression, or classifiers. Though one would hope to simply use...... ordinary Rn-transfer learning ideas, the manifold structure prevents it. We overcome this by basing our method on inner-product-preserving parallel transport, a well-known tool widely used in other problems of statistics on manifolds in computer vision. At first, this straightforward idea seems to suffer...... “commutes” with learning. Consequently, our compact framework, applicable to a large class of manifolds, is not restricted by the size of either the training or test sets. We demonstrate the approach by transferring PCA and logistic-regression models of real-world data involving 3D shapes and image...
Quaternionic Kaehler and hyperkaehler manifolds with torsion and twistor spaces
International Nuclear Information System (INIS)
Ivanov, Stefan; Minchev, Ivan
2001-12-01
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(l) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor, thus connecting two structures arising from quantum field theories and supersymmetric sigma models with Wess- Zumino term. We discovered that a HKT manifold has always co-closed Lee form. Applying this property to compact HKT manifold we get information about the plurigenera. (author)
Convex functions and optimization methods on Riemannian manifolds
Udrişte, Constantin
1994-01-01
This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...
Investigating performance of microchannel evaporators with different manifold structures
Energy Technology Data Exchange (ETDEWEB)
Shi, Junye; Qu, Xiaohua; Qi, Zhaogang; Chen, Jiangping [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, No. 800, Dongchuan Rd, Shanghai 200240 (China)
2011-01-15
In this paper, the performances of microchannel evaporators with different manifold structures are experimentally investigated. Eight evaporator samples with 7 different designs of the I/O manifold and 5 different designs of the return manifold are made for this study. The performances of the evaporator samples are tested on a psychometric calorimeter test bench with the refrigerant 134A at a real automotive AC condition. The results on the variations of the cooling capacity and air temperature distribution of the evaporator due to the deflector designs in the I/O manifold and flow hole arrangements in the return manifold are presented and analyzed. By studying the KPI's for the performance of an evaporator, the design trade-off for an evaporator designer is summarized and discussed. (author)
Directory of Open Access Journals (Sweden)
Hui Zhang
2017-01-01
Full Text Available The control of vortex-induced vibration (VIV in shear flow with different distributions of Lorentz force is numerically investigated based on the stream function–vorticity equations in the exponential-polar coordinates exerted on moving cylinder for Re = 150. The cylinder motion equation coupled with the fluid, including the mathematical expressions of the lift force coefficient C l , is derived. The initial and boundary conditions as well as the hydrodynamic forces on the surface of cylinder are also formulated. The Lorentz force applied to suppress the VIV has no relationship with the flow field, and involves two categories, i.e., the field Lorentz force and the wall Lorentz force. With the application of symmetrical Lorentz forces, the symmetric field Lorentz force can amplify the drag, suppress the flow separation, decrease the lift fluctuation, and then suppress the VIV while the wall Lorentz force decreases the drag only. With the application of asymmetrical Lorentz forces, besides the above-mentioned effects, the field Lorentz force can increase additional lift induced by shear flow, whereas the wall Lorentz force can counteract the additional lift, which is dominated on the total effect.
International Nuclear Information System (INIS)
Bolte, J.
1992-08-01
The Selberg trace formula for automorphic forms of weight m ε- Z, on bordered Riemann surfaces is developed. The trace formula is formulated for arbitrary Fuchsian groups of the first kind which include hyperbolic, elliptic and parabolic conjugacy classes. In the case of compact bordered Riemann surfaces we can explicitly evaluate determinants of Maass-Laplacians for both Dirichlet and Neumann boundary-conditions, respectively. Some implications for the open bosonic string theory are mentioned. (orig.)